50 CT15 Abstracts

IP1 munications (direct messages sent between the agents) can Stochastic Target Problems complement each other and lead to simple distributed control algorithms with remarkably good performance. We In these class of optimization problems, the controller tries close by discussing the role of communication and influ- to steer the state process into a prescribed target set with ence connectivities and the need for new non-commutative certainty. The state is assumed to follow stochastic dynam- probability models to model and analyze humans in such ics while the target is deterministic and this miss-match networked systems. renders the problem difficult. One exploits the degenera- cies and/or the correlations of the noise process to deter- John Baras mine the initial positions from which this goal is feasible. Univ. Maryland These problems appear naturally in several applications in College Park quantitative finance providing robust hedging strategies. [email protected] As a convenient solution technique, we use the geometric dynamic programming principle that we will describe in IP4 this talk. Then, this characterization of the reachability sets will be discussed in several examples. Irreversibility in Dynamic Optimization

Halil Mete Soner Irreversibility is the property that characterizes evolution- ETH Zurich ary processes which do not allow for time inversion. In [email protected] Dynamic Optimization, such a behavior is expected for noise-perturbed systems but it also takes place in the deterministic case: being able to solve the Hamilton-Jacobi IP2 equation forward in time from some initial data and then backward, resulting in the same data, often implies the so- A Convex Optimization Approach to Infinite- lution is smooth. Analyzing these phenomena may help Dimensional Systems to exploit optimization techniques in their full strength. Time-delay appears naturally in many control systems. It This talk will discuss irreversibility effects such as the gain is frequently a source of instability although, in some sys- of regularity of solutions, the loss of regularity due to the tems, it may have a stabilizing effect. A time-delay ap- onset and persistance of singularities, and compactness es- proach to sampled-data control, which models the closed- timates for the flow. loop system as continuous-time with delayed input/output, Piermarco Cannarsa has become popular in the networked control systems University of Rome ”Tor Vergata”, Italy (where the plant and the controller exchange data via com- [email protected] munication network). Many important plants (e.g. flexible manipulators and heat transfer processes) are governed by PDEs and are described by uncertain nonlinear models. In IP5 this talk Lyapunov-based methods for time-delay and dis- Hybrid Processes for Controlling Manufacturing tributed parameter systems leading to finite-dimensional Systems Linear Matrix Inequalities (LMIs) will be presented. The LMI approach provides an effective and simple tool for ro- Revolutionary computing technologies are driving signifi- bust control of uncertain infinite-dimensional systems. cant advances in the manufacturing domain. High-fidelity simulations and virtual design environments allow unprece- Emilia Fridman dented opportunities to test and validate systems before Tel Aviv University, Israel they are built, reducing overall design time and cost. Tor- [email protected] rents of data streaming from the factory floor can be col- lected over high-speed networks, and stored in large-scale server farms (such as cloud-based systems), enabling im- IP3 proved analytics and increased performance. This talk will Simple Distributed Control of Networked Systems: describe how the integration of simulation and plant-floor Learning, Direct and Indirect Communications data can enable new control approaches that are able to optimize the overall performance of manufacturing system We consider collaborative decision making and control in operations. multi-agent systems. The emphasis is to derive simple distributed algorithms that work provably very well, while Dawn Tilbury having minimal knowledge of the system and its parame- University of Michigan, USA ters; thus the need for learning. We consider a behavior [email protected] learning algorithm for a class of behavior functions and study its effects on the emergence of agent collaboration. Next we consider systems, with each agent picking actions IP6 from a finite set and receiving a payoff depending on the Averaged Control actions of all agents. The exact form of the payoffs is unknown and only their values can be measured by the re- This lecture is devoted to address the problem of control- spective agents. We develop a decentralized algorithm that ling uncertain systems submitted to parametrized pertur- leads to the agents picking welfare optimizing actions uti- bations. We introduce the notion of averaged control ac- lizing the impact of agents actions on their payoffs, and if cording to which the average of the states with respect needed very simple bit-valued information exchanges be- to the uncertainty parameter is the quantity of interest. tween the agents. We next consider the continuous time We observe that this property is equivalent to a suitable and continuous state space version of the problem based averaged observability one, according to which the initial on ideas from extremum seeking control. Our results show datum of the uncertain dynamics is to be determined by how indirect communications (signaling between the agents means of averages of the observations done. We will first via their interactions through the system) and direct com- discuss this property in the context of finite-dimensional CT15 Abstracts 51

systems to later consider Partial Differential Equations, [email protected] mainly, of wave and parabolic nature. This analysis will lead to unexpected results on the robustness of observabil- N. Sukavanam ity estimates with respect to additive perturbations. We IIT Roorkee, Roorkee shall also highlight that the averaging process with respect [email protected] to the unknown parameter may lead a change of type on the PDE under consideration from hyperbolic to parabolic, for instance, significantly affecting the expected control theo- CP1 retical properties. We shall link these results to well-known phenomena on regularisation by averaging. We will also Controlled Invariance and Dynamic Feedback for present some open problems and perspectives of future de- Systems over Semirings velopments. This work has been developed in collaboration with J. Lohac, M. Lazar and Q. Lu. The concept of (A, B)-invariant subspace is the fundamen- Enrique Zuazua tal concept of the geometric approach of control design. Ikerbasque & Basque Center for Applied Mathematics It has been extended by many authors to that of (A, B)- (BCAM invariant module or semimodule, for the sake of extending [email protected] the solution of various control problems to the case of systems over rings or semi rings. In this paper is discussed the use of dynamic feedback control laws for systems over SP1 semirings, and it is shown that an (A, B)-invariant semi- W.T. and Idalia Reid Prize in Mathematics Lec- module over a commutative semiring can be made invariant ture: Definitions and Hypotheses and All That for the closed-loop system by dynamic feedback. Stuff Jean Jacques Loiseau, Carolina Cardenas, Claude There are times when a satisfactory analysis of a problem Martinez in control requires certain abstract tools which may ap- IRCCyN Nantes, CNRS pear somewhat esoteric at first. In this non technical talk, [email protected], carocarde- we illustrate this proposition with some examples in which [email protected], [email protected] lack of existence, non smooth behavior, and discontinuous feedback are involved. CP1 Francis Clarke Université Claude Bernard Lyon 1, France Normal Forms of Linear Multivariable Square Sys- [email protected] tems and Their Application

SP2 Normal forms called by Byrnes-Isidori are useful to study properties of zeros of controlled systems in continuous-time SIAG/CST Prize Lecture - Control of Higher Or- and sampled-data domain for the design of feedback con- der PDEs: KdV and KS Equations trollers. This paper investigates how transfer function matrices and state-space equations of linear square systems Higher-order PDEs appear to model different nonlinear are transformed to normal forms, and applies the results propagation phenomena. This class of equations in- to analysis of zeros of sampled-data models corresponding cludes the Korteweg-de Vries (KdV) and the Kuramoto- to continuous-time linear square systems nondecouplable Sivahinsky (KS) equations. The first one is dispersive while by static state feedback. the second one is parabolic. In despite of this great difference, they have in common some important features. For instance, both of them present critical spatial domains for Mitsuaki Ishitobi, Sadaaki Kunimatsu which the boundary controllability does not hold. In this Kumamoto University talk we aim at explaining the main results and methods [email protected], [email protected] concerning the control and stabilization of these nonlinear u.ac.jp one-dimensional PDEs.

Eduardo Cerpa CP1 UTDSM - Universidad T´ecnica Federico Santa Mara [email protected] Diﬀerential Controllability and Observability Func- tions with Applications to Model Reduction

CP1 In this talk, we aim at constructing a nonlinear balancing Approximate Controllability of Second Order method in the contraction framework. We introduce the Semilinear Stochastic System with Variable Delay notion of differnetial controllability and observability func- in Control and with Nonlocal Conditions tions, and we provide characterizations for them. Then, we define the differential balanced realization and study This paper deals with the approximate controllability of model reduction for such a realization. second Order semilinear stochastic system with variable delay in control and with nonlocal conditions. The result is obtained by using Banach fixed point theorem. At the Yu Kawano end, an example is given to show the effectiveness of the Kyoto Univ. result. [email protected]

Urvashi Arora Jacquelien M. Scherpen IIT Roorkee Rijksuniversiteit Groningen 52 CT15 Abstracts

[email protected] [email protected], sergey.dashkovskiy@fh- erfurt.de

CP1 Relative Controllabilty Properties CP2 For nonlinear systems described by ordinary differential On Reduced Order Observer for Radiative Conduc- equations, we present the notion of W -control sets which tive Heat Transfer Systems are defined as maximal subsets of complete approximate controllability within a safe region or world W in the state This contribution deals with state observer design for a space. In articular, their relative invariance properties and class of non-linear coupled partial differential equations their behavior under parameter variations are character- that describe radiative-conductive heat transfer systems in ized. An application to invariance entropy shows that the 2D (two dimension). Observations are made though sen- information needed to keep a system in a subset of the state sors placed at the upper boundary of the two dimensional space is determined by the relatively invariant W -control domain. We explored the Galerkin method for a semi- sets. discretization to obtain a large scale in finite dimensional. Thanks to the special structure of the obtained state sys- Ralph Lettau tem, we show through the Differential Mean Value Theo- University of Augsburg rem that there always exists an observer gain matrix that Research Unit Applied Analysis assures asymptotic convergence. Both full order and re- [email protected] duced order state estimators are provided.

Fritz Colonius Mohamed Ghattassi University of Augsburg IECL-University of Lorraine [email protected] [email protected]

Mohamed Boutayeb, Jean Rodolphe Roche CP1 University of Lorraine Nonlinear Unknown Input Observability: Analyti- [email protected], jean- cal Expression of the Observable Codistribution in [email protected] the Case of a Single Unknown Input

This paper investigates the unknown input observability CP2 for nonlinear systems characterized by a single unknown input and multiple known inputs. The goal is not to design Instability Characterizations for Differential Inclu- new observers but to provide a simple analytic condition sions to check the observability of the state. In other words, the goal is to extend the observability rank condition to Instability of an equilibrium point has typically been de- the case of unknown input. As in the case of only known fined as “not stable” rather than as a standalone property. inputs, the observable codistribution is obtained by recur- This is, in part, due to the fact that several unstable be- sively computing Lie derivatives along the vector fields that haviors are possible. Furthermore, as the usual engineering characterize the dynamics. However, in correspondence of goal is stability, all possible unstable behaviors are undesir- the unknown input, the corresponding vector field must be able. In this talk, we present some specific definitions for rescaled. Additionally, the Lie derivatives must be also unstable equilibrium points for differential inclusions. We computed along a new set of vector fields that are ob- also present Lyapunov characterizations and discuss their tained by recursively performing suitable Lie bracketing utility in a control design context. of the vector fields that define the dynamics. The analytic approach is illustrated by checking the weak local observ- Christopher M. Kellett ability of several nonlinear systems driven by known and University of Newcastle unknown inputs. [email protected] Agostino Martinelli INRIA [email protected] CP2 Characterizations of Input-to-State Stability for CP2 Infinite-Dimensional Systems Modelling and Stability for Interconnections of Hy- This talk is devoted to Lyapunov characterizations of brid Systems the input-to-state stability (ISS) property for infinite- Robustness and stability theory of hybrid systems is dimensional control systems. We discuss Lyapunov charac- strongly developed recently, however interconnections of terizations of uniform asymptotic stability for systems with such systems are poorly studied. The existing few results disturbances and establish connections between the asymp- hold under strong constraints on jump and flow sets of totic gain property, uniform global asymptotic stability of subsystems only. General type interconnections are not undisturbed systems and ISS. Using the above criteria it is well developed and raise many modelling and mathemati- possible to characterize input-to-state stability in terms of cal problems. We will discuss these problems and possible ISS Lyapunov functions. solutions with emphasis on stability properties. Andrii Mironchenko, Fabian Wirth Petro Feketa, Sergey Dashkovskiy University of Passau University of Applied Sciences Erfurt [email protected], fabian.wirth@uni- CT15 Abstracts 53

passau.de not completely solve, the energy czars problem.

James Case CP2 Consultant Eigenvectors of Nonlinear Maps on the Cone of [email protected] Positive Semidefinite Matrices and Application to Stability Analysis CP3 We show that the problem of synthesis of a common Lya- Trajectory Optimization and Performance-Based punov function for some classes of switched linear systems Vehicle Guidance in Spatiotemporally Varying can be approached by solving an eigenproblem involving Fields a nonlinear map on the cone of positive semidefinite matrices. This map involves the selection of a maximal lower We discuss planar trajectory optimization where the cost bound of a family of matrices in this cone. We present some functional is the integral along the trajectory of the inten- variants of the power algorithm, allowing one to solve the sity of a spatiotemporally-varying scalar field. We assume nonlinear eigenproblem in a scalable way. that this spatial field is described by an advection-diffusion parabolic PDE or a Poisson-type elliptic PDE. Multiresolu- Nikolas Stott tion spatiotemporal discretization is employed for numer- INRIA - CMAP, Ecole Polytechnique ical trajectory optimization and for concurrent estimation [email protected] of the field by a mobile sensor. Single- and twin-agent scenarios will be considered.

Xavier Allamigeon Raghvendra V. Cowlagi CMAP, Ecole Polytechnique Assistant Professor, Worcester Polytechnic Institute [email protected] Worcester, MA, USA [email protected] St´ephane Gaubert INRIA-Saclay & CMAP Michael A. Demetriou Ecole Polytechnique Worcester Polytechnic Institute [email protected] [email protected]

Eric Goubault, Sylvie Putot LIX, Ecole Polytechnique - CNRS CP3 [email protected], [email protected] On the Optimal Control of the Rigid Body Pre- cise Movement: Is Energy Optimality the Same as Time Optimality? CP3 A New Inverse Optimal Control Method for For optimal control problems of rigid body precise move- Discrete-Time Systems ment minimal time optimality and minimal energy optimality are considered as competing approaches for trajec- This paper presents a new approach based on extended tory planning. We investigate here theoretical and sim- kalman filter to construct a control lyapunov function. This ulation results showing that, with appropriate choice of function will be used in establishing the inverse optimal constraints, these approaches are equivalent in the sense controller. The main aim of the inverse optimal control that they produce the same trajectory. The optimal con- method is to avoid the solution of HamiltonJacobiBellman trol solver DIDO was used as a numerical tool. equation resulted from the traditional solution of nonlinear optimal control problem. The relevance of the proposed Per-Olof Gutman scheme is illustrated through simulations. Results show Faculty of Civil and Environmental Engn the effectiveness of the proposed method. Technion-Israel Institute of Technology [email protected] Moayed N. Almobaied Istanbul technical university Ilya Ioslovich http://www.itu.edu.tr/en/home Faculty of Civil and Environmental Engineering [email protected] Technion-Israel Institute of Technology [email protected] Ibrahim Eksin, Mujde Guzelkaya Istanbul Technical University Shail Moshenberg Control and Automation engineering Faculty of Civil and Environmental [email protected], [email protected] Engineering, Technion [email protected] CP3 The Energy Czar’s Problem CP3 Optimal Control of Landfills Consider an island economy powered in part by renewable energy, and in part by a single deposit of fossil fuel. The We tackle landfill optimization when the re-circulation islands energy czar, who wishes to make the best possible leachate is the control. We propose a scheme to construct use of the endowment, faces an optimal control problem not the minimal time strategy by dividing the state space into unlike the one confronting the proprietor of an extractive three subsets. On two of them the optimal control is confirm. The latter problem has an extensive history, which stant until reaching target, while it can exhibit a singular will be summarized. Existing results shed light on, but do arc on their complementary. The singular arc could have 54 CT15 Abstracts

a barrier, and we prove the existence of a switching curve obtained . that passes through a point of prior saturation. Charkaz A. Aghayeva Alain Rapaport Institute of Cybernetics of ANAS, Azerbaijan INRA Anadolu University, Turkey [email protected] [email protected]

Térence Bayen CP4 University Montpellier II, France Geometric Methods for Optimal Sensor Design [email protected] Optimal estimation and control of linear systems are fun- Matthieu Sebbah damental to many areas of engineering and beyond. It is UTFSM, Valparaiso, Chile well-known that the optimal estimator in the MSE sense is [email protected] the Kalman filter., the performance of which depends on the observation matrix (C matrix) of the system. In this Andres Donoso-Bravo presentation, we address the problem of finding the obser- CIRIC, Inria Chile vation matrix that yields the lowest estimation error. This [email protected] problem is non-convex, but we show almost global convergence to a global minimum in an appropriate regime. Alfredo Torrico Mohamed Ali Belabbas CMM, Santiago, Chile University of Illinois [email protected] [email protected]

CP3 CP4 Minimal-Time Bioremediation of Water Resources On Discrete Time Optimal Portfolio for Continuous with Two Patches Time Market Models

We study the bioremediation, in minimal time, of a water We present an algorithm of optimal multistock portfolio resource using a single continuous bioreactor connected to selection in the class of piecewise constant portfolios that two pumps at different locations in the resource. This leads can be restructured at a sequence of random times. We to a minimal-time optimal control problem whose control suggest to separate selection of an optimal redistribution variables are the inflow rates of both pumps, obtaining a of the risky stocks and the optimal distribution of funds non-convex problem. We solve the problem by applying between risk free investment and the risky portfolio, This Pontryagin’s principle to the associated generalized control leads to a discrete time myopic optimal portfolio strategy. problem and obtain explicit bounds on its value function Nikolai Dokuchaev via Hamilton-Jacobi-Bellman techniques. Curtin University [email protected] Victor Riquelme DIM, Universidad de Chile, Santiago, Chile, Université Montpellier 2, Montpellier, France. CP4 [email protected] Stochastic Optimal Control with Delay in the Con- trol: Solution Through Partial Smoothing Héctor Ram´ırez C. DIM and CMM, Universidad de Chile, Stochastic optimal control problems governed by delay Santiago, Chile equations with delay in the control are more difficult to [email protected] study than the the ones when the delay appears only in the state. The associated HJB equation does not satisfy Alain Rapaport the so-called “structure condition’ which means that “the INRA noise enter the system with the control’. The absence of [email protected] such condition, together with the lack of smoothing properties which is a common feature of problems with delay, prevents the use of the known techniques to prove the exis- CP4 tence of regular solutions. In this paper we provide a result on existence of regular solutions of such kind of HJB equa- Stochastic Control Problem for Delayed Switching tions and we use it to solve completely the corresponding Systems with Restrictions control problem finding optimal feedback controls. The main tool used is a partial smoothing property that we In this talk we consider optimal control problem for prove for the transition semigroup associated to the un- stochastic systems. Dynamic of the system is described controlled problem. Such results holds for a specific class by the collection of stochastic differential equations with of equations and data which arises naturally in many ap- delay. We have investigated the stochastic control system plied problems. which consist of several subsystems and a switching law in- dicating the active subsystem at each time instantly. The Fausto Gozzi restrictions is defined by the functional inclusions in the Luiss University right ends of each time interval. Firstly, optimality condi- [email protected] tion for control system without constraints is established. Then using Ekelands Variational Principle, the necessary Federica Masiero condition of optimality for restricted stochastic systems is Università di Milano Bicocca CT15 Abstracts 55

[email protected] Block S17, 10 Lower Kent Ridge Road, Singapore 119076 [email protected]

CP4 Optimal Resource Extraction in Regime Switching CP5 Lévy Markets Multigrid Preconditioning for Space-Time Dis- tributed Optimal Control Problems Constrained This paper studies the problem of optimally extracting by Parabolic Equations nonrenewable natural resources in light of various financial and economical restrictions and constraints. Taking into We present some recent results regarding multigrid pre- account the fact that the market values of the main natural conditioning of the linear systems arising in the solution resources i.e. oil, natural gas, copper, gold, fluctuate ran- process of space-time distributed optimal control problems domly following global and seasonal macro-economic pa- constrained by parabolic equations. While the construction rameters, these values are modeled using Markov switching of the preconditioners is based on ideas extracted from op- Lévy processes. We formulate this problem as a finite-time timal control problems constrained by elliptic equations, in horizon combined optimal stopping and optimal control the parabolic-constrained case the multigrid precondition- problem. We prove that the value function is the unique ers exhibit a suboptimal behavior, namely they approxi- viscosity solution of the corresponding Hamilton-Jacobi- mate the operators to be inverted by half an order less Bellman equations, and derive optimal extraction policies. than optimal. Moreover, we prove the convergence of a finite difference approximation of the value function. Numerical examples Andrei Draganescu, Mona Hajghassem are presented to illustrate these results. Department of Mathematics and Statistics University of Maryland, Baltimore County Moustapha Pemy [email protected], [email protected] Towson University Department of Mathematics [email protected] CP5 A Semi-Analytical Solution for the Helmholtz Problem in Three-Dimensional Case CP4 Stochastic Markov Decision Subject to Ambiguity This paper develops an analytical solution for sound, electromagnetic or any other wave propagation described by In this presentation we address optimality of stochastic the Helmholtz equation. First, a theoretical investigation control strategies for infinite-horizon Markov decision prob- based on Multipole Expansion method was established. lems with discounted pay-off, when the controlled process Then, we evaluate numerically the theoretical solution of conditional distribution belongs to a ball of radius R with scattering problem by an ideal rigid sphere. Finally, we respect to total variation distance, centered at the nominal made a numerical study to present the variation of surface conditional distribution. The stochastic control problem potential with respect to different physical parameters of is formulated using minimax theory and the following dy- the problem. namic programming equation is obtained Layouni Amamou Manel o R v(x)= inf f(x, u)+α v(z)Q (dz|x, u)+α sup v(z)−Rueinf Jommav(z) . Gharsallah, Touza 5023, Tunisie. u∈U(x) X 2 z∈X [email protected]∈X Here, v(x) is the value function, U(x) is the feasible con- o trol set, f is the one stage cost, Q (·|x, u) is the nominal CP5 ∈ controlled process conditional distribution and, α (0, 1) Comparison between the MINC and MRMT Con- is the discounting factor. figurations: The n-dimensional Case

Ioannis Tzortzis, Charalambos D. Charalambous The models MINC (Multiple INteracting Continua) and Dept of Electrical and Computer Engineering, Univ. of MRMT (Multiple Rate Mass Transfer) are extensively used Cyprus in transport phenomena. We believe that these models are [email protected], [email protected] also relevant to describe flows in soil or in porous media. In the same way, these models can be used to describe con- CP5 nections between bioreactors. The goal of this manuscript is determine conditions for the input-output equivalence of Computing the Hamiltonian Triangular Forms of these configurations for n compartments using some results Hamiltonian Pencils of the linear system theory. This paper presents a new method for computing the − Alejandro Rojas-Palma Hamiltonian triangular form of a Hamiltonian pencil λE Departamento de Ingeniera Matemática, Universidad de A with E,A ∈ R2n×2n without purely imaginary eigenval- 3 Chile ues. The algorithm is of computational complexity O(n ), [email protected] and it is based on orthogonal-symplectic transformations and thus preserves the Hamiltonian structure of the pencil λE − A. Problems in the existing benchmark collection for Alain Rapaport the discrete-time algebraic Riccati equations are used to INRA illustrate the performance of the proposed algorithm. [email protected]

Delin Chu Jean-Raynald Dreuzy (de) Department of Mathematics, National University of Geosciences Rennes, UMR CNRS 6118, Rennes, France Singapore IDAEA-CSIC, Barcelona, Spain. 56 CT15 Abstracts

[email protected] Morocco brouri [email protected] Héctor Ram´ırez Centro de Modelamiento, Matemático-Universidad de Chile CP6 [email protected] Frequency-Domain Performance Analysis of Distributed-Parameter Systems under Periodic Sampled-Data Feedback Control CP5 Extracting Motion Primitives Toward Planning The stability and performance of distributed-parameter Human-Like Motions systems operating under periodic sampled-data feedback control is studied via integral-quadratic constraint (IQC) The motions of entities can be thought of as either short- based analysis. Sufficient frequency-domain conditions or long-term motion primitives: fragments of movements are derived for verifying a specified bound on the L2- that embody one or more significant actions. We present a gain of the feedback interconnection of a plant with (ir- means of quickly and automatically extracting these promi- rational) Callier-Desoer class transfer function and a feed- nent actions from long sequences of human movement and back controller obtained via the periodic sample-and-hold pose data. We show that dynamical-systems-based char- discretization of a finite-dimensional LTI controller. The acterizations of these primitives can be used to efficiently analysis is underpinned by a time-varying delay model of plan paths for a highly articulated humanoid platform. the sample-and-hold operation and IQC characterizations of a related system. An illustrative numerical example in- Isaac J. Sledge volving the control of a linear system of hyperbolic conser- Department of Electrical and Computer Engineering vation laws is presented. University of Florida isledge@ufl.edu Chung-Yao Kao National Sun Yat-Sen University, Taiwan Kamran Mohseni [email protected] University of Florida, Gainesville, FL mohseni@ufl.edu Michael Cantoni University of Melbourne [email protected] CP5 Regulation Pitch Angle of Wind Turbine Using Reference Model Adaptive Controller CP6 Optimization of Synchronization Gains in Net- The conversion of wind energy to electrical energy with worked Distributed Parameter Systems wind turbine is one of the best ways for reduction of harm- ful effects of fossil fuels. The renewable energy is growing We consider networked distributed parameter systems that rapidly in all over the world. Controlling blade pitch angle are tasked with synchronization. Synchronization con- is a suitable way to achieve desired power of the turbine at trollers based on static output feedback are used to ensure low speed winds and in order to prevent damages in strong synchronization. Using both tracking and synchronization wind conditions. In this paper, pitch angle control in dif- metrics, the gain optimization problem is formulated as a ferent wind conditions by using Reference Model Adaptive minimization of a quadratic performance index. The op- (RMA) Controller is proposed. Simulations and numerical timal gains are then found as the ones that minimize the results show that the output power control and pitch angle trace to the solution of a parameter-dependent operator based on RMAC has faster nominal value with less error. Lyapunov equation for the aggregate system.

Alireza Yazdizade Michael A. Demetriou Shahid Beheshti University Worcester Polytechnic Institute A [email protected] [email protected]

CP6 CP6 Frequency Identiﬁcation of Wiener-Hammerstein Right Coprime Factorizations for Fractional Sys- Systems. tems with Input Delays

The problem of identifying Wiener-Hammerstein systems The design of robust control laws lies in the computation is addressed in the presence of two linear subsystems of of left and right coprime factorizations over the ring of structure totally unknown. Presently, the nonlinear ele- complex functions that are analytic in the right complex ment is allowed to be noninvertible. The system identifica- plane. In her recent thesis, the third author (by alpha- tion problem is dealt by developing a two-stage frequency betic order) described a method to compute left coprime identification method such a set of points of the nonlin- factorizations for a class of fractional systems with input earity are estimated first. Then, the frequency gains of delays. Here is proposed a method to compute right co- the two linear subsystems are determined at a number of prime factorizations. The method is based on the concept frequencies. The method involves Fourier series decom- of column-reduced matrix, that already proved to be use- position and only requires periodic excitation signals. All ful to solve this problem in the case of finite dimensional involved estimators are shown to be consistent. systems.

Adil Brouri Jean Jacques Loiseau ENSAM, AEEE departm, L2MC, Moulay Ismail IRCCyN Nantes, CNRS University, Meknes [email protected] CT15 Abstracts 57

Catherine Bonnet Judy Day Team DISCO, INRIA Saclay, France University of Tennessee [email protected] [email protected]

Le Ha Vy Nguyen Seddik Djouadi Team DISCO, INRIA Saclay University of Tennessee at knoxville and Math. Dept., Univ. Namur Department of Electrical engineering and computer [email protected] science [email protected]

CP6 Flow Sensing and Control for Aerospace Vehicles CP7 Characterization of the Hemodynamic Response in Aerospace vehicles move in a fluid such as water or air, the Brain using Observer which can be moving relative to an inertial frame. The movement of fluid over the vehicle impacts the dynamics Cerebral blood flow (CBF) is a key physiological variable and control of translational and rotational motion. To im- in understanding the hemodynamic response in the brain prove control performance, the flow can be characterized which gives a deep insight into the underlying dynamics in real time by assimilating spatially distributed measure- of brain activation. We propose an observer-based ap- ments of pressure and/or velocity. The design and use of proach to estimate CBF from blood oxygen level dependent flow sensing arrays for underwater and aerial vehicles will (BOLD) signal measured using functional magnetic reso- be described. nance imaging. The model describing the pathway from CBF to BOLD is a coupled system of partial and ordi- Derek A. Paley nary differential equations (PDE/ODE). Numerical results University of Maryland will be presented to show the accuracy of the estimation Dept. Aerospace Engineering and Inst. for Systems method. Research [email protected] Zehor Belkhatir Computer, Electrical and Mathematical Sciences and Engineering, KAUST CP6 [email protected] On Robust Output Regulation for Continuous- Time Periodic Systems CP7 Optimal Dosing Strategies Against Susceptible and We construct a controller to solve robust output tracking Resistant Bacteria problem for a stable linear continuous-time periodic system on a finite-dimensional space. We begin by transforming Antibiotic modelling is concerned with the problem of find- the time-dependent plant to a time-invariant discrete-time ing efficient and successful dosing techniques against bac- system using the “lifting technique’. The controller is then terial infections. In this study, we model the problem of designed to achieve robust output tracking for the lifted treating a bacterial infection where the bacteria is divided system. We show that the solution of the control problem into two sub-populations: susceptible and resistant. The for a continuous-time periodic system necessarily requires susceptible type may acquire the resistance gene via the an error feedback controller with an infinite-dimensional process of conjugation with a resistant bacterium cell. Ef- internal model. The results are illustrated with an exam- ficient treatment strategies are devised that ensure bac- ple where robust output tracking is considered for a stable teria elimination while minimizing the quantity of antibi- periodic scalar system. otic used. Such treatments are necessary to decrease the chances of further development of resistance in bacteria Lassi Paunonen and to minimize the overall treatment cost. We consider Department of Mathematics the cases of varying antibiotic costs, different initial bac- Tampere University of Technology terial densities and bacterial attachment to solid surfaces, lassi.paunonen@tut.fi and obtain the optimal strategies for all the cases. The results show that the optimal treatments ensure disinfection for a wide range of scenarios. CP7 Parameter Estimation for Nonlinear Immune Re- Mudassar Imran sponse Model Using Em Arizona State University [email protected] The problem of parameter estimation of reduced mathematical model of the acute inflammatory response is considered for the discrete case in the presence of disturbances CP7 and measurement noise. A method combining expectation A Mathematical Analog of Muscular Hydrostats maximization and particle filter is introduced. the param- and Similar Tissues eters that characterize each virtual patient are of interest. We begin with a study of nonlinear observability of the Muscular hydrostats (tongues, trunks, and tentacles) are system to justify the use of state estimation and finally we composed almost of muscles which can shorten themselves present some simulation and discuss the obtained results. but require a force external to the muscle to lengthen. This external force is supplied by the internal pressure Ouassim Bara that maintains the constant volume of the structure. A University of Tennessee at knoxville very simplified mathematical description of such a system [email protected] is proposed and its response to various controls is computed 58 CT15 Abstracts

and displayed. Curling a tentacle, a trunk, or a tongue is from strong limitations. Here, we present significant im- demonstrated. provements and report numerical results. A method of contour optimization is provided. It is based on a theo- William S. Levine retical error estimate of the solution. Finally, we discuss University of Maryland, College Park expected gains if the method is implemented on different [email protected] parallel computer topologies. The envisioned applications are for real-time distributed control on distributed computing architectures. CP7 A Variable Reference Trajectory for Model-Free Raphael Couturier Glycemia Regulation IUT Belfort-Montbéliard [email protected] The control design of an artificial pancreas, which is a hot research topic for diabetes studies, is tackled via the newly introduced model-free control and its corresponding intelli- CP8 gent proportional controller, which were already quite suc- On Controllability of a Two-Dimensional Network cessful in many concrete and diverse situations. It results of Ferromagnetic Ellipsoidal Samples in an insulin injection for type 1 diabetes which displays via constant references a good nocturnal/fasting response, In this article, we address the problem of stability and but unfortunately poor postprandial behavior due to long controllability of two-dimensional network of ferromagnetic hyperglycemia. When a variable reference is introduced, particles of ellipsoidal shapes. The control is the magnetic that switches between a constant one, when glycemia is field generated by a dipole whose position and amplitude more or less normal or moderate, and an exponential decay can be selected. In the absence of control, first we prove the reference path, when a high glycemia rate indicates a meal exponential stability of the relevant configurations of the intake, the results in silico, which employ real clinical data, network. Then, we investigate the controllability by the become excellent. We obtain a bolus-shaped insulin injec- means of external magnetic field induced by the magnetic tion rate during postprandial phases. The hyperglycemic dipole. peaks are therefore lowered a lot. Sharad Dwivedi, Shruti Dubey Taghreed Mohammadridha Indian Institute of Technology Madras PhD student at IRCCyN-Ecole Centrale de Nantes [email protected], [email protected] [email protected]

Claude Moog CP8 LUNAM, IRCCyN (CNRS, UMR 6597) Analysis of the Push-Sum Algorithm for Unreliable Nantes-France Networks [email protected] In multi-agent systems, the push-sum algorithm allows Emmaneul Delaleau computing the average of values held by the agents in a de- Institut Superieur de lElectronique et du Numerique centralized way. Unlike classical methods, push-sum also (ISEN) works when communications are directed or asynchronous. Brest-France When the network is unreliable, the computed value will [email protected] deviate from the true average. We analyze the error of the final common value obtained, both theoretically and numerically, and compare it with the standard consensus Michel Fliess algorithm. LIX (CNRS, UMR 7161) Ecole polytechnique-Paris ALIEN(Algebre pour Identification & Estimation Balázs Gerencsér, Julien Hendrickx Numeriques) Université catholique de Louvain michel.fl[email protected] [email protected], [email protected] Cedric Join CRAN (CNRS, UMR 7039), Universite de Lorraine-Nancy CP8 ALIEN(Algebre pour Identification & Estimation Minimal Data Rates and Entropy in Digitally Net- Numeriques) worked Systems [email protected] In digitally networked control systems the assumption of classical control theory that information can be transmit- CP8 ted instantaneously, lossless and with arbitrary precision is Diffusive Realization of a Lyapunov Equation So- violated. This raises the question about the smallest data lution, and Parallel Algorithms Implementation rate above which a given control task can be solved. For the problem to render a subset Q of the state space invariant, In a previous work, a theoretical framework of diffusive the minimal data rate can be described by an entropy-like realization for state-realizations of some linear operators quantity, the so-called invariance entropy. If one consid- have been developed. Those are solutions to certain linear ers a single feedback loop and assumes that the system is operator differential equations posed in one-dimensional completely controllable and uniformly hyperbolic on Q,the bounded domains. They illustrate the theory on a Lya- invariance entropy can be expressed in terms of Lyapunov punov equation arising from optimal control theory of the exponents. For networks with several subsystems there are heat equation. In principle their method might be very different possibilities to formulate the question about the efficient for real-time computation, however it is suffering smallest data rate for the invariance problem, but also in CT15 Abstracts 59

this setting entropy-like quantities can be introduced to [email protected] solve the problem.

Christoph Kawan CP9 Institute of Mathematics Sampling Intervals Enlargement for a Class of University of Augsburg Parabolic Sampled-Data Observers [email protected] Enlarging the sampling intervals in the networked control- Jean-Charles Delvenne estimation is a hot topic. Presently, we seek sampling in- Université Catholique de Louvain terval enlargement for sampled-data observers designed for Applied Mathematics Department a class of parabolic systems. This purpose is shown to be [email protected] achievable by using inter-sample output predictor based observers. Sufficient conditions for global exponential convergence are derived in terms of LMIs via Lyapunov- CP8 Krasvoskii functionals. It is checked through simple examples that the proposed observers considerably enlarge Real-Time Decentralized and Robust Voltage Con- the sampling interval. The results are illustrated by some trol in Distribution Networks examples from the literature. Voltage control plays an important role in the operation Tarek Ahmed-Ali of electricity distribution networks, especially when there GREYC Lab is a large penetration of renewable energy resources. In ENSICAEN this paper, we focus on voltage control through reactive ahmed [email protected] power compensation and study how different information structures affect the control performance. In particular, we Emilia Fridman first show that using only voltage measurements to deter- Tel Aviv University, Israel mine reactive power compensation is insufficient to main- [email protected] tain voltage in the acceptable range. Then we propose two fully decentralized and robust algorithms by adding additional information, which can stabilize the voltage in the Fouad Giri acceptable range. The one with higher complexity can fur- GREYC Lab ther minimize a cost of reactive power compensation in a Université de Caen Basse-Normandie particular form. Both of the two algorithms use only local [email protected] measurements and local variables and require no communication. In addition, the two algorithms are robust against Fran¸coise Lamnabhi-Lagarrigue heterogeneous update rates and delays. LSS CNRS SUPELEC Guannan Qu, Na Li [email protected] Harvard University [email protected], [email protected] CP9 Munther Dahleh Reduced Order Modelling for Optimal Cancer MIT Treatment [email protected] We study reduced order modelling for optimal treatment planning. Boltzmann transport equation is used to model the interaction between radiative particles with tissue. At CP8 first, we solve optimization problems: minimizing the de- Topological Obstructions to Distributed Feedback viation from desired dose distribution. Then we consider a Stabilization to a Submanifold parameterized geometry. In offline stage we solve a problem for sampled parameter values. The online phase then We consider the problem of local asymptotic feedback sta- consists of solving the reduced problem for the actual set bilization – via a C1 feedback law – of a control system n 1 of parameters. Theoretical and numerical results are pre- x˙ = f(x, u) defined in Euclidean space R (with f ∈ C ) sented. to a compact, connected, oriented p−dimensional submanifold P of Rn, subject to the constraint that the scalar Bahodir Ahmedov entries of the system function f and of the feedback law u Aachen Institute for Advanced Study in depend only on selected subsets of the state variables. Such Computational Engineering Science (AICES) constraints arise naturally in the context of distributed con- [email protected] trol systems, typically consisting of multiple agents with only local communication between the various agents. We Michael Herty, Martin Grepl obtain topological necessary conditions for the existence RWTH Aachen University of such a stabilizing feedback control law; these topologi- [email protected], [email protected] cal conditions are expressed in terms of the generators of the homology groups of certain topological spaces naturally associated with the control problem, as well as the CP9 topology of the submanifold to which stabilization is to be Some Numerical Extension for the LOI/BOI Ap- performed. proach for the Control of de Saint-Venant Equa- tions in Infinite Dimension Abdol-Reza Mansouri Department of Mathematics and Statistics This paper considers the control design of a nonlinear dis- Queen’s University tributed parameter system in infinite dimension, described 60 CT15 Abstracts

by PDEs of de Saint-Venant. The nonlinear system dy- perbolic PDEs namic is formulated by a Multi-Models approach over a wide operating range, where each local model is defined We investigate the problem of bilinear control of a solar around a set of operating regimes. A PI feedback was de- collector plant using available boundary and solar irradi- signed and performed through Bilinear Operator Inequality ance measurements. The solar collector is described by a and Linear Operator Inequality techniques for infinite di- first-order 1D hyperbolic partial differential equation where mensional systems. The authors propose in this paper to the pump volumetric flow rate acts as the control input. improve the numerical part by introducing weight μi not By combining a boundary state observer and an internal only equal to {0,1}, but μi ∈ [0, 1]. energy-based control law, a nonlinear observer based feedback controller is proposed. The effect of solar radiation is Valerie Dos Santos Martins cancelled using a feed-forward control term. UniversityClaudeBernandofLyon1 LAGEP Sarah Mechhoud, Shahrazed Elmetennani, Meriem Laleg [email protected] KAUST [email protected], Mickael Rodrigues [email protected], taous- Université Claude Bernard Lyon 1 [email protected] [email protected] CP10 CP9 Rigorous Numerical Method for Irrigation Canal Optimal Damping Coefficient of a Slowly Rotating System Dynamics and Control Timoshenko Beam Water canals for water delivery or irrigation provide a This paper continues the authors previous investigations challenging system dynamics and control problem for dis- of stability of the slowly rotating Timoshenko beam whose tributed parameter plants. Water pool dynamics are de- movement is controlled by the angular acceleration of the rived from the shallow water equations (also called Saint- disk of the driving motor into which the beam is rigidly Venant equations in its one-dimensional form) that are a clamped. We consider the problem of optimal value of set of hyperbolic partial differential nonlinear equations. damping coefficient of a particular type of viscoelastic Rigorous numerical methods that are able to capture wa- damping operator. To determine location of spectrum of ter wave dynamics in canals are difficult to achieve. In this an appropriate operator we use a transfer function method. case a numerical routine was designed from a finite volume method for hyperbolic systems of conservation laws Mateusz Firkowski with source terms using a semi-discrete MUSCL flux re- University of Szczecin construction linear well-balanced scheme. Time integra- fi[email protected] tion was done with a Runge-Kutta method. The numerical method was used to simulate water dynamics in the first two pools with withdraws of an existing irrigation canal in Jaroslaw Wozniak Vila Nova de Mil-Fontes, Portugal, including PI controlled University of Szczecin gates movement to compensate for wave disturbances. Dep. Mathematics and Physics [email protected] JoséIgreja ISEL INESC-ID CP9 [email protected] Asymptotic Behavior for Coupled Abstract Evolu- tion Equations with One In?nite Memory CP10 In this work, we consider two coupled abstract linear evo- Preconditioned Continuation Model Predictive lution equations with one in?nite memory acting on the Control ?rst equation. Under a boundeness condition on the past history data, we prove that the stability of our abstract Model predictive control (MPC) anticipates future events system holds for convolution kernels having much weak to take appropriate control actions. Nonlinear MPC decays than the exponential one considered in the liter- (NMPC) describes systems with nonlinear models and/or ature. The general and precise decay estimate of solution constraints. A Continuation/GMRES Method for NMPC, we obtain depends on the growth of the convolution kernel suggested by T. Ohtsuka in 2004, uses GMRES iterative al- at in?nity and the regularity of the initial data. We also gorithm to solve a forward difference approximation Ax = b present various applications to some hyperbolic distributed of the Continuation NMPC (CNMPC) equations on every coupled systems such as wave-wave, Petrovsky-Petrovsky, time step. The coefficient matrix A of the linear system wave-Petrovsky and elasticity-elasticity. These results have is often ill-conditioned, resulting in poor GMRES conver- been published in Applicable Analysis, 2014. gence, slowing down the on-line computation of the control by CNMPC, and reducing control quality. We adopt Aissa Guesmia CNMPC for challenging minimum-time problems, and im- Institut Elie Cartan de Lorraine, Université de Lorraine prove performance by introducing efficient preconditioning, Bat. A, Ile du Saulcy, 57045 Metz cedex 01, France utilizing parallel computing, and substituting MINRES for [email protected] GMRES.

Andrew Knyazev CP9 Mitsubishi Electric Research Labs (MERL) Observer-based Bilinear Control of First-order Hy- [email protected] CT15 Abstracts 61

Yuta Fujii als. We will demonstrate how fast or accelerated gradient Advanced Technology R&D Center, Mitsubishi Electric methods can be advantageously employed to solve these Co. problems very efficiently. [email protected] Timm Treskatis, Miguel Moyers-González, Chris Price Alexander Malyshev School of Mathematics and Statistics Mitsubishi Electric Research Labs (MERL) University of Canterbury [email protected] [email protected], [email protected], [email protected] CP10 Anfis Based Software Development for Nonlinear CP10 with Time Delay Dynamic Systems Identification A Kind of Formula For Computing the Matrix This article aims to show a software that was developed to Function identify nonlinear dynamical systems with time delay using the ANFIS. Therefore, we conducted two tests in the In this paper we employ the symbolic computation to de- software, a simulated test uses a benchmark function, the rive a kind of formula for computing the matrix function Mackey-Glass, for making the prediction of future values f(A). of time series. The second test was performed using a real system coupled tanks with a smooth nonlinearity and time Zhinan Zhang delay for the purpose to identify the dynamics of the sys- College of Mathematics and System Science tem. The results shown in this paper confirm the capability Xinjiang University, Xinjiang, P.R.China of the developed software to identify nonlinear, with time [email protected] delay, dynamic systems on a simple and intuitive way, as it was proposed. CP11 JoséK.Martins,Fábio Souza, Fábio Arajo New Results on Stochastic Consensus Networks Universidade Federal do Rio Grande do Norte Departamento de Engenharia da Computa¸cão e We revisit the genera linear time varying consensus prob- Automa¸cão lem and provide new conditions for asymptotic agreement jk kleiton@hotmail.com, [email protected], on the agents’ states on two distinct types of stochastic [email protected] versions of the distributed algorithm. The first type is a linear discrete time dynamic evolution with connectivity signals driven by a measure preserving dynamical system. CP10 Our result highlights the fact that the probabilistic na- New Approach to Implicit Systems and Applica- ture of the connections among agents that imposes almost tions in Control Methods for Optimal Design Prob- sure convergence to consensus actually reproduces the de- lems terministic recurrent connectivity condition known in the literature. The second type, is a linear continuous time Implicit representations of domains are at the core of fixed flocking model with multiple time-varying diffusion coeffi- domain methods in shape optimization, like control meth- cients. Via a stability in variation argument we establish ods or the fictitious domain approach. When the govern- sufficient conditions for asymptotic flocking with coordi- ing equation has Dirichlet boundary conditions, there are nation around around a random-variable. Our analysis is already known results in this respect. In the case of Neu- based on rate at which the diffusion compartment vanishes. mann boundary conditions or of boundary observation, a We argue, by example, that our results treat a number of more detailed knowledge of the properties of the unknown related models proposed in the literature, as special cases. (implicitly defined) boundaries is necessary. We shall present a new approach based on implicit parametrizations of the boundaries. It also allows the handling of the critical Christoforos Somarakis case via the generalized solutions. We consider a class of The Institute For Systems Research variations of the unknown shapes, called functional varia- University of Maryland, College Park tions, similar to the Dirichlet case and show how to com- [email protected] pute directional derivatives of the unknown geometry. John Baras Dan I. Tiba Univ. Maryland Institute of Mathematics, Romanian Academy College Park Bucharest, Romania [email protected] [email protected]

CP11 CP10 A Projection-Based Dual Algorithm for Fast Com- Accelerated Gradient Methods for Elliptic Optimal putation of Control in Microgrids Control Problems with Tv-Regularised Cost We present a novel algorithm for the distributed computa- Over the past years, first order gradient methods have re- tion of optimal predictive storage and reactive power con- gained significant attention. Algorithms like FISTA are trol in microgrids. This algorithm uses a dual decomposi- applicable to a broad range of scenarios, converge quickly tion approach to deal with coupling constraints, and a pri- and are ideally suited for large-scale problems. In this talk, mal projection procedure to handle local constraints. This we consider optimal control problems governed by ellip- significantly decreases the amount of iterations needed for tic equations, with a focus on non-smooth cost function- practical convergence, as compared to the dual decomposi- 62 CT15 Abstracts

tion algorithm involving all constraints. Simulations com- in order to assess the role of each agent and channel within pare the algorithm with the dual decomposition approach a network. Finally, we discuss the emergence of fundamen- in four different testbeds, to show how the speed of con- tal tradeoffs on the performance measure with respect to vergence is improved. the effects of structured noises in different elements of the network. Andres Cortes University of California, San Diego Milad Siami, Sadegh Bolouki, Nader Motee [email protected] Lehigh University [email protected], [email protected], [email protected] Sonia Martinez University of California, San Diego Department of Mechanical and Aerospace Engineering CP11 [email protected] Robust Dynamic Tolls for Self-Interested Traffic Routing

CP11 We consider the problem of designing robust taxation- mechanisms for influencing self-interested behavior in Nullspace Design of Configuration Matrices for routing-problems where users have unknown sensitivities Lyapunov-Based, Multi-Vehicle Control to taxes. Classical results are not sufficient for addressing Lyapunov potential functions are common in multi-vehicle this question due to unrealistic assumptions on either the control algorithms because they ensure vehicle coordi- system condition (i.e., homogeneous known sensitivities) nation while incorporating inter-vehicle communication or available information (i.e., network demands and users topologies. However, this control approach often requires sensitivities). Accordingly, we present a dynamic tolling all vehicles to converge to a desired phase or shape variable. mechanism that, using local feedback, provably guarantees This talk will present recent results toward the design of system-wide optimal behavior for a well-studied class of novel quadratic functions for prescribed coordination. By routing-problems. designing quadratic terms based on matrices with a de- Andreas Wachter sired nullspace, we derive multi-vehicle control algorithms University of Stuttgart steering vehicles to any relative configuration. University of Colorado at Boulder Levi DeVries [email protected] United States Naval Academy Department of Weapons and Systems Engineering Jason Marden [email protected] University of Colorado, Boulder [email protected]

CP11 CP12 Convergence of Iterative Co-Learning Control Optimal Inventory in Failure-Prone Manufacturing This talk discusses iterative co-learning where multiple lin- Systems with Monomial Holding Costs ear subsystems update their input simultaneously based on the error in a common desired output. A challenge is that The optimal policy for the production plan for a single convergence of iterative learning for each individual sub- commodity in a failure-prone parallel machine system is system (when the other subsystems are not learning) may determined by solving the corresponding Hamilton-Jacobi- not guarantee convergence under co-learning. Co learn- Bellman (HJB) equation. The system is assumed to possess ing with an update-partitioning approach will be presented two levels of operation capacity and the surplus holding that guarantees convergence whenever the individual, iter- cost is a monomial function. In this paper the analytical ative learning for each subsystem is convergent. method based on Akella and Kumar (1986) is developed to solve the HJB equation using the derived boundary condi- Santosh Devasia tions of the value function. The effect of different operating University of Washington parameters, such as failure rate, repair rate, maximal ca- [email protected] pacity level, et. al., on the optimal inventory level and the value function are numerically computed by using our analytical formula. For an arbitrary hold cost with the an- CP11 alytical or empirical formula which can be approximated by Role of Structured Noise in Emergence of Funda- the sum of monomial functions, thus this paper provides mental Tradeoffs in Linear Dynamical Networks a way to construct the corresponding optimal production plan. We deal with a network of multiple agents with dynamics described by a continuous time linear consensus algo- Huang-Nan Huang rithm. The performance of the network in presence of var- Department of Mathematics ious types of noise inputs is investigated. We adopt the ex- Tunghai University pected steady-state dispersion of the states of the network [email protected] as a performance measure. The relationship between this performance measure and characteristics of the underlying Shu-Yi Tu graph of the network is explored. Specifically, we quantify Mathematics Department, University of Michigan-Flint how the asymptotic behavior of a linear consensus network sytu@umflint.edu is influenced by the existence of structured noises in different elements of the network, such as noise in sensors, emitters, channels, receivers, and the computational unit. CP12 In the next step, a class of centrality measures is introduced Performance Bound for Approximate Dynamic CT15 Abstracts 63

Programming in Borel Spaces [email protected]

We consider discrete-time constrained Markov control processes (MCPs) for Borel state and action spaces. We CP12 present a two-stage method to approximate the optimal Distributed Optimization Based on Multi-Agent value of the constrained MCPs via finite-dimensional con- Systems vex optimization programs. The main contribution of this study is to provide explicit error bounds for the proposed First, a continuous-time multi-agent system with nonlin- solution under mild assumptions which are investigated for ear coupling is proposed to solve distributed optimization the long-run discounted as well as average cost. Finally, we problems. Sufficient conditions are derived to ascertain also discuss the performance of the approximated control the convergence to optimal solutions. The nonlinear cou- policy. pling can deal with bounded inputs for agents and limited bandwidth for communication among agents. Fur- Peyman Mohajerin Esfahani thermore, the nonlinear coupling has a superior property Swiss Federal Institute of Technology (ETH) in Zurich of robustness against additive noise than the linear case. [email protected] Next, communication delays are considered on multi-agent systems for distributed optimization. Based on optimality conditions, it is revealed that optimal solutions are corre- Tobias Sutter sponding to the equilibrium points in a positive invariant ETH Zurich set of the time-delay system. Both delay-dependent and [email protected] delay-independent sufficient conditions are derived for as- certaining convergence to optimal solutions in the case of Daniel Kuhn slow-varying delay. Delay-dependent conditions are also Ecole´ Polytechnique Fédérale de Lausanne presented for the case of fast-varying delays. daniel.kuhn@epfl.ch Jun Wang, Shaofu Yang John Lygeros The Chinese University of Hong Kong ETH Zurich [email protected], [email protected] [email protected] Qingshan Liu Huazhong University of Science & Tech. CP12 [email protected] Improvements to Optimal Control Problem Solvers on the Example of a Reachable Set Algorithm CP13 Output Feedback H-infinity Control for Discrete- The reachable set at a given time T of a nonlinear control Time Singular Systems: A Strict LMI Approach system is the union of endpoints of all feasible solutions. The talk illustrates how an OCP-solver can be applied to This paper deals with the problem of the output feedback calculate discrete reachable sets and shows some strategies H∞ control for discrete-time singular systems. Our goal is to increase the stability of the OCP-solver for this class of to develop a numerically tractable controller design method problems. Furthermore a subdivision approach to improve for output feedback H∞ control of discrete-time singular the performance of the algorithm will be introduced. systems. First, a new sufficient condition for H∞ performance is derived. Then, a sufficient condition for the Wolfgang Riedl existence of the desired output feedback H∞ controller is Department of Mathematics established. The proposed controller design method is for- University of Bayreuth mulated under the strict LMI framework. Finally, a nu- [email protected] merical example is used to demonstrate the effectiveness of presented method.

CP12 Shyh-Feng Chen China University of Science and Technology Convex Methods for Rank-Constrained Optimiza- [email protected] tion Problems

Consider a rank-constrained optimization problem, which CP13 is otherwise convex. Penalizing the nuclear norm of the Parameterization of Positively Stabilizing Feed- matrix minimizes its rank. We introduce a convex con- backs for Single-Input Positive Systems straint, which, when used in conjunction with the above penalty, results in a convex problem that usually yields so- For unstable positive finite-difference systems approximat- lutions of exactly desired rank. A modified dual program ing a diffusion PDE system with Neumann boundary con- finds the ”best” value of the parameter used with the nu- ditions and scalar boundary input, parameterizations of all clear norm. It is shown that allowing negative valued pa- positively stabilizing state feedbacks are derived.They are rameters (rewarding the nuclear norm) can result in better based on characterizations of stable Metzler matrices by performance. The methods are demonstrated on SDPs. LMIs and of polyhedral sets as finitely generated cones, respectively.With well-chosen parameter values, this process Michael Rotkowitz, Van Sy Mai, Dipankar Maity, generates a Dirac sequence of feedback functionals yielding Bhaskar Ramasubramanian a limit feedback such that the resulting closed-loop PDE Electrical and Computer Engineering system is positive and stable. University of Maryland, College Park [email protected], [email protected], [email protected], rb- Jonathan N. Dehaye,JosephJ.Winkin 64 CT15 Abstracts

University of Namur, Department of Mathematics Rapha¨el Jungers Namur Center for Complex Systems (naXys) Universit´e Catholique de Louvain, [email protected], [email protected] ICTEAM/INMA [email protected]

CP13 On the Construction of Continuous Suboptimal CP13 Feedback Laws Convexity + Curvature: Tools for the Global Stabi- lization of Nonlinear Systems with Control Inputs It is well known that optimal feedback laws are usually dis- Subject to Magnitude and Rate Bounds continuous functions on the state, which yields to ill-posed closed loop systems and robustness issues. In this talk we The aim of this paper is to address the global asymptotic show a procedure for the construction of a continuous sub- stabilization (GAS) of affine systems with control inputs optimal feedback law that allows overcoming the aforesaid subject to magnitude and rate bounds, in the framework problems. The construction we exhibit depends exclusively of Artstein-Sontag’s control Lyapunov function (CLF) ap- on the initial data that could be obtained from the optimal proach. These bounds are defined by compact (convex) feedback. control value sets (CVS) U with 0 ∈ intU.ConvexAnaly- sis together with Differential Geometry allow us to reveal Cristopher Hermosilla the intrinsic geometry involved in the CLF stabilization ENSTA ParisTech problem, and to solve it, if an optimal control ω(x) exists. [email protected] The existence and uniqueness of ω(x) depends on convexity properties of CVS U; whereas its regularity and bounded- Fabio Ancona ness of its differential is achieved in terms of the curvature Università degli Studi di Padova of U. However, in view that control ω(x) is singular, we [email protected] redesign it to derive an explicit formula for regular damping feedback controls fulfilling magnitude and rate bounds that render GAS a class of affine systems. CP13 A Topological Method for Finding Positive Invari- Julio Solis-Daun ant Sets Universidad Autonoma Metropolitana - Iztapalapa [email protected] A usual way to find invariant sets of a differential system is to impose that the flow goes inward on the border of the set. Using a topological approach (and in particular CP14 Wazewskis property) we present an algorithm that is based Thermostatic Approximation of Optimal Control on a sufficient and weaker combinatorial condition of the Problems on Multi-Domains flow on the border. We start from a template polyhedron and prove the positive invariance of a subset in the interior We study an optimal control problem with two controlled of this template. different dynamics in two half-spaces, in the framework of HJB equations. We introduce an approximation by the use Sameh Mohamed of switching rules of the delayed-relay type, and study the LSV (ENS Cachan) and LIX (Ecole Polytechnique) passage to the limit when the parameter of the approxima- [email protected] tion (i.e. the thresholds distance) goes to zero. We then compare our result with other ones from the recent litera- Laurent Fribourg ture. Finally, we briefly sketch a one-dimensional threefold LSV (E.N.S Cachan) junction problem. [email protected] Fabio Bagagiolo, Rosario Maggistro Sylvie Putot, Eric Goubault Department of Mathematics, University of Trento, Italy LIX, Ecole Polytechnique - CNRS [email protected], [email protected] [email protected], [email protected] CP14 CP13 Necessary Optimality Conditions for the Time of A Graph-Related Sufficient Condition for the Ex- Crisis Control Problem. act Computation of the Joint Spectral Radius We consider a non-smooth optimal control problem where Our talk relates to the stability analysis of discrete-time the cost functional represents the time of crisis, that is, the switching systems, with and without logical switching con- time spent by a solution of a control system outside a given traints. We present an efficiently checkable sufficient con- set. A regularization scheme of the problem based on the dition under which a quadratic multiple Lyapunov function Moreau-Yosida approximation is proposed. We prove the has a contractivity factor equal to the joint spectral radius convergence of an optimal sequence for the approximated of a system. This allows us to exactly compute its joint problem to an optimal solution of the original one. We spectral radius in finite time. We put our work in rela- derive optimality conditions on the original and regularized tion with the previously introduced finite-time algorithm problem. of Guglielmi and Protasov. Terence Bayen Matthew Philippe University of Montpellier Université Catholique de Louvain, [email protected] ICTEAM/ INMA [email protected] Alain Rapaport CT15 Abstracts 65

INRA University of Melbourne [email protected] [email protected]

CP14 CP14 Optimal Control Methods for Solving Laser Param- Optimal Boundary Control of Process Described eter Extraction Problem by the System of Telegraph Equation

There are a wide range of applications involving laser prop- In the present paper we study the problem boundary con- agation through a scattering medium. Very often, a mea- trol of oscillations described by the system of telegraph surement of the scattered light will be taken with the intent equations: of learning some information about the medium. On the contrary, the present work seeks to extract a description of ux + Lit + Ri =0,ix + Cvt + Gu =0 the source of light and its location. A phenomenological in rectangle QT =[0≤ x ≤ l] × [0 ≤ t ≤ T ]. model for off-axis intensity is presented which employs a − Mie scattering aerosol database. The model is extended to Where i(x, t)-current strength, u(x t) – voltage in a two- predict the off-axis polarized light described by the Stokes wire transmission line with distributed parameters: resis- vector. Several inversion techniques are given and analyzed tance(R),capacity(C), charge leakage(G),self-induction(L). as well as example problems detailed which can recover the Will be found the explicit form of boundary control range, direction, power and polarization of the laser source. u(0,t)=μ(t),u(l, t)=0 Current work on solving off-axis laser detection problem as an optimal control problem for the Radiative Transfer which transfers the system from a given initial state Equation is also discussed. u(x, 0) = φ1(x),i(x, 0) = ψ1(x) Vaibhav Kukreja Naval Postgraduate School to a given final state [email protected] u(x, T )=φ2(x),i(x, T )=ψ2(x)

CP14 for a predetermined period of time T. Boundary control New Sufficient Condition for the Proto-Lipschitz provides a minimum the following energy functional Continuity of the State Constrained Bilateral Min- T imal Time Function it(0,t)ut(0,t)dt We provide a sufficient condition for the proto-Lipschitz 0 continuity of the state constrained bilateral minimal time . function. Compared with the sufficient conditions given in C. Nour and R. J. Stern, The state constrained bilat- Ilya Smirnov eral minimal time function, Nonlinear Anal., 69, no. 10, Lomonosov Moscow State University 3549-3558, (2008), our new condition does not impose any [email protected] geometric assumption on the constraint set S and does not involve points exterior to S. CP15 Chadi Nour Dynamic Risk Measures for Finite-State Partially Lebanese American University Observable Markov Decision Problems Department of Computer Science and Mathematics [email protected] We provide a theory of time-consistent dynamic risk measures for finite-state partially observable Markov decision problems. By employing our new concept of stochastic con- CP14 ditional time consistency, we show that such dynamic risk Eigenvalue Assignment for Systems with Multiple measures have a special structure, given by transition risk Time-Delays mappings as risk measures on the space of functionals on the observable state space only. Moreover, these mappings We consider the problem of pole assignment for a linear enjoy a strong law invariance property. time invariant plant with state feedback subject to multiple time delays in the control input. For systems with a known Jingnan Fan, Andrzej Ruszczynski time delay, we offer a parametric formula for the feedback Rutgers University gain matrix that will assign a desired set of closed-loop [email protected], [email protected] eigenvalues to the time-delay system. We consider some well-established pole placement methods for systems without delay that utilise pole placement via state feedback in CP15 order to achieve their desired performance objective. We The Sakawa-Shindo Algorithm in Stochastic Con- explore the extent to which their desired control perfor- trol mance objective may be successfully achieved for a time- delay system by placing the primary poles of the delayed In this work, J.F. Bonnans, J. Gianatti and F.J. Silva. The system at the same locations as for the system without Sakawa-Shindo Algorithm in stochastic control. Preprint, delay. The role of the secondary poles of the time-delay to appear, we study the extension to the stochastic case system will also be investigated since they are known to of a first order algorithm for solving deterministic optimal affect both the stability and performance. control problems proposed by Y. Sakawa and Y. Shindo. On global convergence of an algorithm for optimal control. Robert S. Schmid IEEE Trans Aut. Control. vAC-25. 1149, 1980, and ana- Department of Electrical and Electronic Engineering lyzed in J.F. Bonnans. On an algorithm for optimal control 66 CT15 Abstracts

using Pontryagin’s maximum principle. SIAM J. Control Memory and Optimization, 24, 1986. We need to assume that either the cost functional is Lipschitz and the volatility term is We consider a stochastic portfolio optimization model in not controlled, or that the dynamics is an affine function of which the returns of risky asset depend on its past per- the state and the control. We prove that the iterates of the formance. The price of the risky asset is described by a algorithm are well defined and the cost function decreases. stochastic delay differential equation. The investor’s goal Moreover, for convex problems we obtain the convergence is to maximize the expected discounted utility by choos- of the iterates in the weak topology. ing optimal investment and consumption as controls. We use the functional Ito’s formula to derived the associated Francisco José Silva Alvarez Hamilton-Jacobi-Bellman equation. For logarithmic and XLIM, Université de Limoges exponential utility functions, we can obtain explicit solu- Université de Limoges tions in a finite dimensional space. [email protected] Tao Pang Department of Mathematics Frédéric Bonnans North Carolina State University Inria-Saclay and CMAP, Ecole Polytechnique [email protected] [email protected] Azmat Hussain Justina Gianatti Operations Research OPTyCON, Universidad Nacional de Rosario North Carolina State University [email protected] [email protected]

CP15 CP15 An (s, s, S) Optimal Maintenance Policy for Sys- Zubov’s Method for Controlled Diffusions with tems Subject to Shocks and Progressive Deterio- State Constraints ration We consider a controlled stochastic system in presence of We define a model of a system that deteriorates as a result state-constraints. Under the assumption of exponential of (i) shocks, modeled as a compound Poisson process and stabilizability of the system near a target set, we aim to (ii) deterministic, state dependent progressive rate, with characterize the set of points which can be asymptotically variable and fixed maintenance cost. We define mainte- driven by an admissible control to the target with positive nance strategies based on an impulse control model where probability. We show that this set can be characterized as time and size of interventions are executed according the a level set of the optimal value function of a suitable un- system state. We characterize the value function as the constrained optimal control problem which in turn is the unique viscosity solution of the HJB equation and prove unique viscosity solution of a second order PDE which can that an (s, s, S) policy is optimal. We also provide numer- thus be interpreted as a generalized Zubov equation. ical examples. Finally, a singular control problem is pro- posedwherethereisnofixedcost,whichstudyandrelation Athena Picarelli with the former problem is open for future discussion. Dipartimento di Matematica, SAPIENZA, Universita’ di Roma Mauricio Junca [email protected] Universidad de los Andes [email protected] Lars Grüne Mathematical Institute Universitaet Bayreuth CP15 [email protected] Two End Points Boundary Value Problems on Stochastic Optimal Transportation and Fokker- CP16 Planck Equation Resolution-Directed Optimization-Based Dis- We give a sufficient condition under which stochastic op- tributed Sensing timal transportation problem is finite, by the finiteness of the supremum in the duality theorem, which implies the In this paper we study the problem of optimal zone cov- existence of a semimartingale with given initial and termi- erage, using distributed sensing, i.e., a group of collabo- nal distributions. It also gives a new approach for h-path rating sensors. We formulate the problem as an optimiza- processes with given initial and terminal distributions. We tion problem with time-varying cost function. We examine also consider the similar problem to above for a class of op- the case where a group of elevated imaging sensors look timal control problems for a family of solutions to Fokker- down to and form the map of a 2-dimensional environ- Planck equations. ment at a pre-specified resolution. The sensors solve an optimization problem that attempts to optimize a time- Toshio Mikami varying cost function. The cost at any time instance mea- Tsuda College sures the distance between the desired resolution function [email protected] and the achieved resolution until the previous time instant. We discuss the numerical implementation challenges of this approach and demonstrate its performance on a numerical CP15 example. An Application of Functional Ito’s Formula to Richard Vaccaro Stochastic Portfolio Optimization with Bounded University of Rhode Island CT15 Abstracts 67

[email protected] Ludovick Gagnon UniversitéParis6 Petros Boufounos, Mouhacine Benosman [email protected] Mitsubishi Electric Research Laboratories [email protected], m [email protected] CP16 Identification of Optimum Parameters in Mathe- CP16 matical Model of Temperature Measuring Device A Localized Proper Symplectic Decomposition We propose the mathematical model describing the depen- Technique for Model Reduction of Parameterized dence of the temperature on the resistances for self-test of Hamiltonian Systems temperature transducer, which is represented as system of equation with unknown degrees and coefficients. Method Recently, a symplectic model reduction technique, to identification of unknown parameters based on regular- proper symplectic decomposition (PSD), is proposed to ization technique is proposed. We obtain the error esti- achieve computational savings for a large-scale Hamil- mates of the solutions to this problem which allows to cal- tonian system while preserving the symplectic structure culate the temperature values with guaranteed accuracy [arXiv:1407.6118]. As an empirical approach, PSD pre- and to develop the criteria to self-test of device. serves system energy and stability, thus, PSD is better suited than the classical POD for model reduction. In this Natalia M. Yaparova, Aleksandr Shestakov talk, we combine PSD with the idea of parameter domain South Ural State University (National Research partition, and propose a localized PSD technique for model University) reduction of parameterized Hamiltonian systems. [email protected], [email protected] Liqian Peng, Kamran Mohseni University of Florida, Gainesville, FL CP16 [email protected], mohseni@ufl.edu An Application of Global Sensitivity Analysis to Large Scale Power System Small Signal Stability

CP16 We propose an application of the variance-based global Numerical Analysis of a Family of Optimal Dis- sensitivity analysis to determine impact of variation of se- tributed Control Problems Governed by An Ellip- lected parameters and their interactions on power system tic Variational Inequality small-signal stability. In practice, such analysis becomes essential when studying impact of increased penetration of The numerical analysis of a family of distributed optimal renewable energy sources on stability. Computation is per- control problems governed by elliptic variational inequali- formed via Tensor-Train cross interpolation to map high- ties (for each α>0) is obtained through the finite element dimensional parameter space to system eigenvalues. For method when its parameter h → 0. We also obtain the each interpolation point, eigenvalues are computed using limit of the discrete optimal solutions when α →∞(for small-signal stability software commonly used in industry. each h>0) and a commutative diagram for two continuous and two discrete optimal solutions are obtained when h → 0andα →∞. Rastko Zivanovic The University of Adelaide Domingo A. Tarzia [email protected] CONICET - Univ. Austral Depto Matematica [email protected] CP17 Approximate Controllability of a Second-Order Mariela Olguin Neutral Stochastic Differential Equation with State Univ. Nac. de Rosario Dependent Delay [email protected] In this paper the conditions for approximate controllability are investigated for a distributed second order neutral CP16 stochastic differential system with respect to the approximate controllability of the corresponding linear system in Uniform Boundary Observability for Polynomial a Hilbert space X. Our hypothesis is described as a ge- Approximations of the Wave Equation ometrical relation in L2(0,T : X) between the range of the operator B and the subspace N ⊥ related with the sine The boundary observability of the second order wave equa- function S(t). Thereby, we remove the need to assume tion is not preserved uniformly with respect to the dis- the invertibility of a controllability operator, which fails to cretization parameter after application of classical approx- exist in infinite dimensional spaces if the associated semi- imation methods like finite differences, finite elements or group is compact. Our approach also removes the need to spectral elements. Here we consider a spectral Legendre- check the invertibility of the controllability Gramian oper- Galerkin (polynomial) space-discretization of the 1-d wave ator and the associated limit condition, which are practi- equation. We show that the uniform observability can be cally difficult to verify and apply. An example is provided recovered using spectral filtering, mixed formulations or a to illustrate the presented theory. Specifically we study the weak imposition of the boundary conditions. following second order equations modelled in the form Jose M. Urquiza d(x (t)+g(t, xt)) = [Ax(t)+f(t, xρ(t,x ))+Bu(t)]dt Centre de Recherches Mathematiques t ∈ Universite de Montreal + G(t, xt)dW (t),a.e.ont J =[0,a] [email protected] x0 = φ ∈B,x(0) = ψ ∈ X (1) 68 CT15 Abstracts

where A is the infinitesimal generator of a strongly con- [email protected] tinuous cosine family {C(t):t ∈ R} of bounded linear operators on a Hilbert space X. The state space x(t) ∈ X F and the control u(t) ∈ L2 (J, U), where X and U are sepa- CP17 rable Hilbert spaces and d is the stochastic differentiation. Continuous-Discrete Observers for Time-Varying Let (Ω, F,P) be a probability space together with a nor- Nonlinear Systems: A Tutorial on Recent Results mal filtration Ft,t≥ 0. Let K be a separable Hilbert space and {W (t)}t≥0 is a given K− valued Brownian motion or Continuous-discrete systems occur when the plant state Wiener process with finite trace nuclear covariance opera- evolves in continuous time but where the output values tor Q>0. The functions f,g : J ×B→X are measurable are only available at discrete time instants. Continuous- mappings in X norm and G : J ×B → LQ(K, X)isa discrete observers have the valuable property that the ob- measurable mapping in LQ(J, X)norm. servation error between the true state of the system and the observer state converges to zero in a uniform way. The Sanjukta Das design of continuous-discrete observers can often be done Indian Institute of Technology, Roorkee, by building framers, which provide componentwise upper sanjukta [email protected] and lower bounds for the plant state. This paper is a tutorial on these approaches, highlighting recent results in the literature, and also providing previously unpublished, orig- Dwijendra Pandey inal results which are not being simultaneously submitted Indian Institute of Technology, Roorkee elsewhere. [email protected] Frederic Mazenc INRIA CP17 [email protected] Resolving the Pattern of Akt Activation by Varia- tional Parameter Estimation Vincent Andrieu LAGEP-UMR 5007 Laboratory, Lyon, France [email protected] Ordinary differential equation models have become one of the pillars for understanding complex biological systems. The equations typically contain many unknown parameters Michael Malisoff such as reaction rates and initial conditions, but also input Louisiana State University functions driving the system. Both are aprioriunknown Department of Mathematics and need to be estimated from experimental data. Here, malisoff@lsu.edu we introduce variational calculus and adjoint sensitivities to apply it for input- and parameter estimation in mam- CP17 malian target of rapamycin (mTOR) signaling. Whereas the direct identification and quantification of different ac- Exact Null Controllability of Evolution Equations tive mTOR complexes is only possible by highly challeng- by Smooth Scalar Controls and Applications to ing experiments, the mathematical framework allows to Controllability of Interconnected Systems reconstruct its dynamics by solving an appropriate Euler- Lagrange equation. The inherently large search space un- The most of papers devoted to controllability problems derlying this approach allows to test specific biological hy- are mainly considering square integrable or piecewise- potheses about the activation of protein kinase B (AKT) continuous controls as a set of admissible controls. How- by mTORC2 and to reject an alternative model with high ever some mechanical systems, for example, cars or air- statistical power. crafts, require smooth controls. Exact null-controllability conditions for abstract linear control equations in the class of smooth controls are presented. One of applications of Daniel Kaschek these results is the exact null-controllability conditions for Institute of Physics, University of Freiburg a series of interconnected equations, governed by a control [email protected] of the last one. These conditions allow us to use the presented abstract approach for a series contained equations of a different structure. For example, the first one may be CP17 a parabolic control equation, and the second one may be a Polynomial Approximations and Controllability of linear differential control system with delays, governed by Time-Invariant Linear Ensemble Systems scalar control, and so on. The exact null-controllability for interconnected heat–wave equations is considered as illustrative example. Robust manipulation of an ensemble of structurally identical dynamical systems is imperative for wide-ranging appli- Benzion Shklyar cations from quantum control to neuroscience. We study Holon Academic Institute of Technology, ensemble control of finite-dimensional time-invariant lin- Holon, Israel ear systems and develop explicit ensemble controllability shk [email protected] conditions. Our derivation is based on the notion of polynomial approximation and the spectra properties of the system matrices. Practical examples and numerical sim- CP17 ulations for optimal control of such ensemble systems are Approximate Controllability of Semilinear Frac- presented to demonstrate the applicability of the theoreti- tional Control Systems of Order α ∈ (1, 2] cal results. The objective of this paper is to present some sufficient Jr-Shin Li conditions for approximate controllability of semilinear de- Washington University in St. Louis lay control systems of fractional order α ∈ (1, 2] . The CT15 Abstracts 69

results are obtained by the theory of strongly continuous lization for neutral delay-differential systems with infinite α-order cosine family and sequential approach under the delay is investigated. Using Lyapunov method, new suf- natural assumption that the linear system is approximate ficient condition for the stability of neutral systems with controllable. At the end, an example is given to illustrate infinite delay is obtained in terms of linear matrix inequal- the theory. ity (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the fea- Anurag Shukla, N Sukavanam, D.N. Pandey sible solution of the resulting LMI, which are easily solved IIT Roorkee using any optimization algorithms. Numerical examples [email protected], [email protected], are given to illustrate the results of the proposed methods. [email protected]

Iyai Davies CP18 Control Theory and Application Centre (CTAC), On the Finite-Time Stabilization of Strings Con- [email protected] nected by Point Mass Olivier Haas In this paper, the problem of finite-time boundary stabi- Coventry University lization of two strings connected by point mass is investi- [email protected] gated. Based on the so-called Riemann invariant transformation, the vibrating strings are transformed in two hybrid-hyperbolic systems, and leads to the posedness of CP18 our system. In order to act in the system, it is desirable to Observer Based Control for a Class of Coupled choose boundary feedbacks, in this case, Hölderien stabi- Parabolic Hyperbolic Systems lizing feedback laws to vanish in finite-time the right and the left of the solutions are considered. This paper investigates the control problem for nonlinear- coupled partial differential equations that describe Chaker Jammazi radiative-conductive heat transfer systems. Thanks to the Ecole Polytechnique de Tunisie special structure of the obtained state system, using the [email protected] Galerkin method for the semi-discretization of PDE and to the differential mean value theorem, a new linear matrix Ghada Ben Belgacem inequality condition is provided for the observer-based con- Ecole Polytechnique de Tunisie, Université de Carthage troller design. The observer and controller gain are com- [email protected] puted simultaneously by solving LMI, i.e a convex problem. Also we provide a reduced order observer based controller that assures global asymptotic stability. CP18 Metzler Matrix Transform Determination Using a Mohamed Ghattassi Nonsmooth Optimization Technique with An Ap- IECL-University of Lorraine plication to Interval Observers [email protected] The paper deals with the design of cooperative observers Mohamed Boutayeb which formulates as computing a state coordinate trans- University of Lorraine form such that the resulting observer dynamics are both [email protected] stable and cooperative. The design of cooperative observers is a key problem to determine interval observers. Solutions are provided in the literature to transform any CP18 system into a cooperative system. A novel approach is pro- On Some System-Theoretic Properties of Hamilto- posed which reformulates into a stabilization problem. A nian Systems Defined on Contact Manifolds solution is found using nonsmooth optimization techniques. The intrinsic description of open irreversible thermodynamic systems has given rise to the definition of control Emmanuel Chambon Hamiltonian systems defined on contact manifolds which Onera - Centre de Toulouse has been call input-output contact systems. In this com- DCSD munication, we shall analyze some system-theoretic prop- [email protected] erties of such systems. We shall, in particular, analyze the structure preserving feedback of these systems, character- Pierre Apkarian ize a class of contact forms achievable in closed-loop and ONERA-CERT consider the stabilization of thse systems. [email protected] Bernhard M. Maschke Laurent Burlion LAGEP, Université Lyon 1, UniversitédeLyon,France Onera - Centre de Toulouse [email protected] DCSD [email protected] CP18 Lyapunov-Razumikhin Methods for Stabilization CP18 in the Sample-and-Hold Sense of Retarded Non- Delay-Independent Closed-Loop Stabilization of linear Systems Neutral Systems with Infinite Delay A new methodology for the design of stabilizers in the Abstract: In this paper, the problem of stability and stabi- sample-and-hold sense for nonlinear retarded systems is 70 CT15 Abstracts

provided. It is shown that, if there exist a control [email protected] Lyapunov- Razumikhin function and an induced steep- est descent state feedback, uniformly in time bounded on bounded subsets of the state space, then such feedback, CP19 applied by suitably fast sampling and holding, guarantees On-Line Model Predictive Control for Constrained practical semiglobal stability, with arbitrary small ﬁnal tar- Image Based Visual Servoing of a Manipulator get ball of the origin.

Pierdomenico Pepe This paper presents an on–line image based visual servo- University of L’Aquila ing (IBVS) controller subject to the constraints based on [email protected] the robust model predictive control (RMPC) method. A controller is designed for the robotic visual servoing system subject to input and output constraints, such as robot CP19 physical limitations and visibility constraints. To verify A Certified Reduced Basis Approach for the effectiveness of the proposed algorithm, real-time ex- Parametrized Linear-Quadratic Optimal Con- perimental results on a 6 Degrees-of-Freedom robot ma- trol Problems with Control Constraints nipulator with eye-in-hand configuration are presented and discussed. We focus at a parameter dependent PDE constrained Op- timal Control Problem with two-sided control constraints. Amir Hajiloo For that problem we derive a model order reduction tech- Department of Mechanical and Industrial Engineering, nique that not only is capable of reducing the optimality Concordia University, Montreal, QC, Canada conditions of the problem but also the control constraints. [email protected] The reduction ensures the strict feasibility for one of the two-sided control constraints and enables us to compute Mohammad Keshmiri, Wen-Fang Xie an approximation and its error bound independently of the Department of Mechanical and Industrial Engineering original dimension of the problem. Concordia University, Montreal, QC, Canada [email protected], Eduard Bader [email protected] Graduate School AICES RWTH Aachen University [email protected] CP19 Analysis of Floating Offshore Wind Turbine Model Mark Kaercher, Martin Grepl Considering Gyro Moment RWTH Aachen University [email protected], A floating offshore wind turbine system is analyzed. First [email protected] we develop the floating offshore wind turbine model and the provide analysis for the dynamics considering the gyro mo- Karen Veroy ment based on the multi-body dynamics analysis. Specif- AICES ically, regarding the blade pitch angle of the rotor as the RWTH Aachen University control input, we derive control laws for the power output [email protected] regulation, floating sway suppression, and gyro-moment suppression at the same time. Furthermore, we provide numerical simulation to show tradeoff relationship between CP19 floating sway suppression and gyro-moment suppression. Maximum Principle for Optimal Control Prob- lems with Integral Equations Subject to State and Tomohisa Hayakawa,RyoAota Mixed Constraints Tokyo Institute of Technology [email protected], [email protected] We consider an optimal control problem with a Volterra type integral equation subject to endpoint equality and inequality constraints, mixed state-control constraints of in- CP19 equality and equality type, and pure state inequality constraints. The gradients of active mixed constraints with Flat Systems of Minimal Differential Weight: Com- respect to the control are assumed to be linear–positively parison Between the Two-Input and the Multi- independent. We prove necessary optimality conditions Input Case which generalize Maximum Principle for similar problems with ODEs. The proof is based on an extension of the con- We study flatness of control-affine systems, defined on an n- trol system by introducing sliding mode controls and using dimensional state-space. In [F. Nicolau and W. Respondek, a relaxation theorem that allows one to approximate solu- Flatness of two-inputs control-affine systems linearizable tions of the extended system by solutions of the original via one-fold prolongation, Nolcos 2013], [F. Nicolau and system. We thus obtain a family of optimal control prob- W. Respondek, Multi-Input Control-Affine Systems Lin- lems with extended systems, for each of which we apply the earizable via One-Fold Prolongation and Their Flatness, stationarity condition (Euler–Lagrange equation, obtained CDC 2013], we gave a complete geometric characterization earlier in our joint work with N.P. Osmolovskii), and then of systems that become static feedback linearizable after a compress these conditions into a universal condition that one-fold prolongation of a suitably chosen control. They has the form of MP. form a particular class of flat systems, that is of differential weight n + m +1,wherem is the number of controls. Andrei V. Dmitruk We distinguished the two-input case, i.e., m =2andthe Central Economics & Mathematics Institute, multi-input case, i.e., m ≥ 3. They have slightly different Russian Academy of Sciences geometries and have to be treated separately. The aim of CT15 Abstracts 71

this talk is to give a comparison between these two cases. [email protected], [email protected]

Florentina Nicolau, Witold Respondek INSA Rouen CP20 ﬂ[email protected], witold.respondek@insa- Robust Optimal Control for Pdes with Uncertainty rouen.fr in Its Input Data

We shall review on recent results obtained by the authors CP19 ([Mart´ınez-Kessler-Periago, Robust optimal shape design Tracking Control of An Underactuated Au- for an elliptic PDE with uncertainty in its input data, to tonomous Ship appear in ESAIM:COCV (2015)] and [Munch-Mart´ınez- Kessler-Periago, in preparation]) concerning robust opti- In this paper, we will construct a control that forces po- mal control problems for elliptic and parabolic partial dif- sition and orientation of the underactuated autonomous ferential equations with uncertainty in its input data. Ro- ship moves according to a reference feasible trajectory. To bustness is modelled by including the variance (and semi- achieve this objective, we use as a design tool of inputs the variance) of the physical quantity to be optimized in the Backtepping methodology and Lyapunov function. Exper- cost functional. For the numerical resolution of the prob- imental results are given to show the tracking performance. lems, the adjoint method is used. Both the direct and we will illustrate trajectories with time varying velocity (si- adjoint (non-local in the probabilistic space) equations are nusoidal path). Then, we will test the tracking robustness solved by using a sparse grid stochastic collocation method. in presence of drag forces disturbances. A number of numerical experiments in 2D will illustrate the theoretical results and will show the computational issues Sarra Samaali, Azgal Abichou which arise when uncertainty is quantified through random LIM, Ecole Polytechnique de Tunisie B.P. 743 - 2078 La fields. Marsa [email protected], [email protected] Francisco Periago, Mathieu Kessler, Jess Mart´ınez-Frutos Universidad Politécnica de Cartagena [email protected], [email protected], CP20 [email protected] HJB Approach to Dynamic Mean-Variance Stochastic Control Arnaud Munch Université Blaise-Pascal We consider a general continuous mean-variance problem [email protected] where the cost functional has an integral and a terminal- time component. We transform the problem into a super- position of a static and a dynamic optimization problem. CP20 The value function of the latter can be considered as the Application of Sufficient Optimality Conditions in solution to a degenerate HJB equation either in viscosity Analysis of Stochastic Models of Illiquid Markets or in Sobolev sense (after regularization) under suitable assumptions and with implications with regards to the op- The purpose of this work is to study the optimal control timality of strategies. problem of an agent in the market with random trade delays. In this article we present a stylized model of optimal Georgios Aivaliotis, Alexander Veretennikov saving and purchases of durable goods in which the mo- University of Leeds ments of time when an agent makes purchases are random [email protected], [email protected] and are described by Poisson flow. We find the optimal behavior of the agent using the sufficient optimality conditions. We prove existence of the solution. In the case of CP20 high intensity of the random process of trade the explicit On Using Spectral Graph Theory to Infer the form of optimal strategy is presented. Structure of Multiscale Markov Processes Aleksandra A. Zhukova Multiscale Markov processes are used to model and control Computing Center of RAS stochastic dynamics across different scales in many appli- Division of mathematical modelling of economy cations areas such as electrical engineering, finance, and [email protected] material science. A commonlyusedmathematicalrepre- sentation that captures multiscale stochastic dynamics is Igor Pospelov that of singularly perturbed Markov processes. Dimen- Computing Center of RAS sionality reductions techniques for this class of stochastic na optimal control problems have been studied for many years. However, it is typically assumed that the structure of perturbed process and its dynamics are known. In this paper, CP21 we show how to infer the structure of a singularly per- Towards a Minimum L2-Norm Exact Control of the turbed Markov process from data. We propose a measure Pauli Equation of similarity for the different states of the Markov process and then use techniques from spectral graph theory to show A computational framework for the exact-control of the that the perturbed structure can be obtained by looking at magnetic state and the spin of an electron is presented. The the spectrum of a graph defined on the proposed similarity evolution of this quantum system is governed by the Pauli matrix. equation, that is a system of Schrödinger equations coupled by the action of magnetic fields. The magnetic fields are Panos Parpas, Chin Pang Ho used as controls in order to steer the quantum system from Imperial College London an initial state to a desired target state at a given final 72 CT15 Abstracts

time. This control framework is based on a minimum norm sponding value function. The value function can be charac- optimization formulation of exact-controllability quantum terized as the solution of a Hamilton-Jacobi Bellman (HJB) problems, that allows the application of efficient Krylov- equation. Besides a low dimensional semi-discretization of Newton optimization techniques. Furthermore, in order to the underlying wave equation it is important to solve the provide this framework with an adequate initialization, a HJB equation efficiently to address the curse of dimen- continuation procedure is discussed. Results of numerical sionality. We propose to apply a semi-Lagrangian scheme experiments demonstrate the effectiveness of the proposed using spatially adaptive sparse grids. Sparse grids allow framework. the discretization of the high(er) dimensional value functions arising in the numerical scheme since the curse of di- Gabriele Ciaramella mensionality of full grid methods arises to a much smaller University of Wuerzburg extent. Several numerical examples are presented. This is [email protected] joint work with J. Garcke (University of Bonn).

Axel Kroener CP21 INRIA Saclay and CMAP, Ecole Polytechnique Optimal Control Via Occupation Measures and In- [email protected] terval Analysis

In this lecture, we present a method based on occupation CP21 measures to compute a guaranteed lower bound to an optimal control problem. Following Vinter approach, the opti- Optimal Motion Planning for Multi-Agent Systems mal control problem is formulate into a linear program- with Uncertainty ming problem of infinite dimension. Thank to Interval arithmetic, this linear programming problem can be ap- Using a computational optimal control approach, a scalable proximate, in a reliable way. Finally, its solution gives a parallel algorithm is developed for optimal motion plan- lower bound to the optimal cost. Examples will illustrate ning involving a large number of interacting heterogeneous the principle of the methodology. agents under uncertainty. The algorithm is tested on designing trajectories of multiple vehicles collectively defend- Nicolas C. Delanoue ing a high-value-unit from hundreds of uncertain attackers. Laris Simulation results demonstrate the efficiency and general- Universitéd’Angers ity of the algorithm for different initial formations, and un- [email protected] der different probability distributions for uncertainty. Ex- tension of the interacting scenarios utilizing Monte Carlo Sebastien Lagrange, Mehdi Lhommeau and Quasi Monte Carlo simulations are discussed. Laris Universitéd’Angers [email protected], Panos Lambrianides, Claire Walton, Qi Gong [email protected] University of California, Santa Cruz [email protected], [email protected], [email protected] CP21 On Approximate Solution of Mobile (scanning) Control Problems CP21 Fast EM Clustering For Large Data Using an In- We describe an approximate technique for solving the so- tegrated Approach Rough-Fuzzy Granulation And called mobile control problems. The method is based on Fisher Discriminate Analysis the Bubnov-Galerkin procedure and allows to reduce the control problem to a finite-dimensional nonlinear system of integral constraints of equality type. An efficient nu- A new fast EM clustering methodology is introduced, based merical scheme is described reducing the solution of the on a combined rough-fuzzy granulation and fisher discrim- nonlinear system to a problem of nonlinear programming. inate analysis (FDA). The proposed algorithm is suitable The proposed method is described for nonlinear equations for mining data sets, which are large both in dimension and with linear boundary conditions. Two particular problems size, in case generation. It utilizes FDA specification and of heating by a moving source and vibration damping by a an granular computing method for obtaining crude initial moving absorber are considered. The system of necessary values of the parameters of the mixture of Gaussians used and sufficient conditions for controllability are obtained in to model the data . Rough set theory is used for feature both cases. Main points of numerical implementations are extraction and solving superfluous attributes issue. Upper discussed. and lower approximations of rough set is calculated based on fuzzy membership functions. Features of a pattern can Asatur Khurshudyan hence be described in terms of three fuzzy membership val- Yerevan State University ues in the linguistic property sets as low (L), medium (M) [email protected] and high (H). FDA provides an optimal lower dimensional representation in terms of discriminating among classes of data. CP21 Towards Optimal Feedback Control of the Wave Hesam Komari Equation Using Adaptive Sparse Grids PWUT [email protected] An approach to solve optimal feedback control problems for the wave equation using adaptive sparse grids is con- Alireza Yazdizadeh sidered. A semi-discrete optimal control problem is intro- Department of Electrical Engineering duced and the feedback control is derived from the corre- Shahid Abbaspour University CT15 Abstracts 73

[email protected] Model Identiﬁcation Search Space Boundary by Standard Genetic Algorithm

CP22 A new predetermined time constant approximation (Tsp) Distributed Controllability of the Wave Equation method for optimising the search space boundaries for an Using Moving Controls optimal model is proposed and presented. Using the dynamic response period and desired settling time offered a This talk aims to address the inner controllability of the better suggestion for initial Tsp values of the transfer func- one dimensional wave equation using controls with sup- tion coefficients. Furthermore, an extension on boundaries ports which may vary with respect to the time variable. derived from the initial Tsp values and the consecutive ex- Theoretical and numerical aspects are considered. A gen- ecution, brought the elite groups within feasible boundary eralized observability inequality for the homogeneous wave regions for better exploration. This enhanced the locating equation is proven and this implies the well-posedness of a of the optimal values of time constant for identified transfer mixed formulation that characterizes the controls of min- function. The Tsp method is investigated on two processes; imal L2 norm. A numerical approximation of this formu- raw data of excess oxygen and a third order transfer func- lation is presented and several numerical experiments are tion model with and without random disturbance. The reported. simulation results assured the Tsp methods effectiveness and flexibility in assisting SGAs to find optimal transfer Nicolae Cindea function model parameters in their explorations. Université Blaise Pascal, Clermont-Ferrand [email protected] Kumaran Rajarathinam Liverpool John Moores University Carlos Castro [email protected] Universidad Politecnica de Madrid [email protected] Barry Gomm, Dingli Yu, ahmed Saad Abdelhadie LJMU Arnaud Münch [email protected], [email protected], Université Blaise Pascal [email protected] Clermont-Ferrand [email protected] CP22 Approximate Optimal Control in Feedback Form CP22 for Parabolic System with Quickly-Oscillating Co- Lpv Control of a Water Delivery Canal with Re- efficients duced Complexity Models In this research, the optimal control in feedback form (syn- The problem of designing a LPV controller for a water de- thesis) was found for linear-quadratic problem that con- livery canal using models with a priori imposed order that sists of semi-defined performance criterion and a parabolic approximate plant dynamics is addressed. A water delivery lumped control system with quickly-oscillating coefficients. canal is an infinite dynamical system that is modelled by The exact formula for the synthesis was found and its the Saint-Venant equations, a pair of hyperbolic partial dif- approximate form that lies in substitution of quickly- ferential equations that embed mass and momentum con- oscillating parameters with average and all infinite sums servation for one-dimensional shallow water streams. Using with finite was justified. a method based on the Laplace transform, these equations References: EGOROV, A. I. Optimal Control of Linear are approximated by a finite dimensional system with a pri- Systems. Kiev: Vishha shkola, 1988. ori imposed order. The fact that the linear approximation Alina Rusina relies on a physical description of the plant allows the quan- Taras Shevchenko National University Of Kyiv tification of the model uncertainty in terms of the physical [email protected] parameters and the order. An LPV controller based on H∞ control is then designed. This work extends recent results of other authors for LPV based on PID laws and CP22 the Muskingum model, by allowing the controller order to be imposed and by providing a direct link with physical Stabilization of Positive Infinite Dimensional Sys- parameters. tems by State Feedback with Cone Constraints on the Inputs Joao M. Lemos INESC-ID, University of Lisbon For positive unstable infinite-dimensional linear systems, [email protected] conditions are established for positive stabilizability and a method is described for computing a positively stabilizing state feedback, which guarantees that the stable Daniela Caiado closed loop dynamics are nonnegative for specific initial INESC-ID, Univ. Lisbon, Portugal states. A feedback control is designed such that the unsta- [email protected] ble finite-dimensional spectrum of the dynamics generator is replaced by the eigenvalues of the stable input dynamics Jose Igreja and such that the resulting input trajectory remains in an INESC-ID, ISEL/IPL, Lisbon, Portugal affine cone. [email protected] Joseph J. Winkin University of Namur, Department of Mathematics CP22 Namur Center for Complex Systems (naXys) Predetermined Time Constant Approximation for [email protected] 74 CT15 Abstracts

M. Elarbi Achhab Jean Clairambault University Choua¨ıb Doukkali, Department of INRIA Paris-Rocquencourt Mathematics [email protected] El Jadida, Morocco [email protected] Emmanuel Trélat Laboratoire Jacques-Louis Lions Universite Pierre et Marie Curie - Paris 6 CP22 [email protected] Stability of the Axially Moving Kirchhoff String with the Sector Boundary Feedback Control CP23 In this study, the stability problem for the axially moving Simultaneous Null Controllability of a Semilinear Kirchhoff string with nonlinear boundary feedback control System of Parabolic Equations has been investigated. The proposed boundary control, which satisfies a sector constraint condition, is a nega- In this paper, we consider a coupled system of two semi- tive feedback of the transverse velocity at the right end linear heat equations. We prove the null controllability of of string. Applying the integral-type multiplier method, the system with a finite number of contraints on the state. the absolute stability of the axially moving Kirchhoff sys- First, we show the equivalence with a null controllability tem is established. To validate the proposed theoretical problem with constrained control. The latter problem was results, numerical simulations are expressed by the finite solved in a previous work, mainly thanks to a crucial ob- element method. servability estimate. Then we use a fixed point theorem to achieve the result. Yuhu Wu, Tielong Shen Sophia University Carole Louis-Rose [email protected], [email protected] Université des Antilles [email protected]

CP23 Convergence Analysis of Hybrid ACO/Nelder- CP23 Mead Tuning Method for PID Controller Struc- The Ribosome Flow Model: Theory and Applica- tures with Anti-Windup tions

A statistical analysis of the system response quality found The Ribosome Flow Model (RFM) is a nonlinear model by Ant Colony Optimization (ACO) based algorithm with describing the movement of ribosomes along the mRNA respect to search space discretization and the ants number strand. We describe the analysis of the RFM using tools is presented for tuning 4 nonlinear controller structures. from systems and control theory including contraction the- The resulting sensitivity curves permit to determine ACO ory, monotone systems theory, and convex analysis. Joint parameter values to initiate Nelder-Mead (NM) algorithm work with Tamir Tuller (Tel Aviv University) and Eduardo which has permitted to reduce the average computation D. Sontag (Rutgers University). time by up to 7 times for an equivalent quality response as compare to the previous ACO-NM algorithm. Michael Margaliot School of Elec. Eng.-Systems Maude Josée Blondin Tel Aviv University UniversitéduQuébec à Trois-Rivières [email protected] [email protected] CP23 Pierre Sicard UniversitéduQuébec à Trois-Rivères Studies on Epidemic Control in Structured Popu- [email protected] lations with Applications to Influenza This work focuses on the dynamics and control of epi- Javier Sanchis Saez demics in age-structured populations over short timescales Universitat Politécnica de València (i.e. single Influenza outbreaks). We study the impact of [email protected] contact structure (i.e. who mixes with whom) and compare the results of a well known empirical study to results generated under the assumption of proportionate mixing. CP23 Finally, we use optimal control theory to identify solutions Optimal Control of Combined Chemotherapies in in the presence of limited vaccine resources. Phenotype-Structured Populations Romarie Morales We consider a system of two scalar integro-differential Arizona State University equations modelling a structured population for healthy [email protected] and tumor cells under the effects of cytotoxic and cyto- static drugs. After having introduced the model and a natural optimal control problem, where the drugs are the CP23 controls to be optimized, we give numerical and analytical Adaptive Polynomial Identification and Optimal results. Tracking Control for Nonlinear Systems Alexander Lorz The paper proposes an adaptive polynomial identifier and a Laboratoire Jacques-Louis Lions robust nonlinear optimal tracking control scheme for poly- Universite Pierre et Marie Curie - Paris 6 nomial systems. The identifier approximates an uncertain [email protected] nonlinear system, where its parameters are on-line adapted CT15 Abstracts 75

using a Kalman-Bucy filter. Then, based on the identifier [email protected] an optimal tracking controller is synthesized, including an integral term to provide it robustness. The identification and control scheme is illustrated via simulations for the CP24 control of the blood glucose level in diabetic patients. Generic Uniqueness of the Bias Vector of Mean- Payoff Zero-Sum Games Fernando Ornelas-Tellez, Angel E. Villafuerte Universidad Michoacana de San Nicolas de Hidalgo Under some ergodicity conditions, finite state space mean [email protected], [email protected] payoff zero-sum games can be solved using a nonlinear fixed point problem, involving a vector (bias or potential), which determines the optimal strategies. A basic issue is to check when the bias is unique. We show that this is always the CP24 case for generic values of the payments of the game. We Using Piecewise-Constant Congestion Taxing Pol- also discuss the application of this result to the perturba- icy in Repeated Routing Games tion analysis of policy iteration. Antoine Hochart We consider repeated routing games with piecewise- INRIA and CMAP, Ecole polytechnique constant congestion taxing in which a central planner sets [email protected] and announces the congestion taxes for fixed windows of time in advance. Specifically, congestion taxes are calcu- Marianne Akian lated using marginal congestion pricing based on the flow of INRIA Saclay–Ile-de-France and CMAP, Ecole the vehicles on each road prior to the beginning of the tax- Polytechnique ing window. The piecewise-constant taxing policy in moti- [email protected] vated by that users or drivers may dislike fast-changing prices and that they also prefer prior knowledge of the prices.Weprovethatthemultiplicativeupdaterulecon- Stéphane Gaubert verges to a socially optimal flow when using vanishing step INRIA-Saclay & CMAP sizes. Considering that the algorithm cannot adapt itself Ecole Polytechnique to a changing environment when using vanishing step sizes, [email protected] we propose using constant step sizes in this case. Then, however, we can only prove the convergence of the dynam- CP24 ics to a neighborhood of the socially optimal flow (with its size being of the order of the selected step size). On Asymptotic Value for Dynamic Games with Saddle Point

Farhad Farokhi We consider two-person dynamic games with zero-sum. We Department of Electrical and Electronic Engineering investigate the limit of value functions of ﬁnite horizon The University of Melbourne games with long run average cost as the time horizon tends [email protected] to inﬁnity, and the limit of value functions of discounted games as the discount tends to zero. Under quite weak as- Karl Johansson sumptions on the game, we prove the Uniform Tauberian ACCESS Linnaeus Center Theorem: existence of a uniform limit for one of the value KTH Royal Institute of Technology functions implies the uniform convergence of the other one [email protected] to the same limit. The key roles in the proof were played by Bellmans optimality principle and the closedness of strategies under concatenation. CP24 Dmitry Khlopin Zero-Sum Stopping Games with Asymmetric Infor- Krasovskii Institute of Mathematics and Mechanics mation [email protected]

We study a model of a two-player, zero-sum, stopping game CP24 with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), A Fractional Mean-Field Game: Existence, where X is only observed by player 1 and Y only by player Uniqueness, and Fast Equilibrium Seeking Algo- 2, implying that the players have access to stopping times rithm with respect to different filtrations. We show the existence of a value in mixed stopping times and provide a varia- In this work, we study a fractional mean-field game prob- tional characterization for the value as a function of the lem given by a fractional controlled state dynamics and initial distribution of the Markov chains. We also prove payoff that measures the gap between a mean-field term a verification theorem for optimal stopping rules in the and the fractional integral of the state. First, we prove that case where only one player has information. (preprint: the problem is well-posed. Second, we show that, given the http://arxiv.org/abs/1412.1412) mean-field term, each decision-maker has a unique mean- field response in the space of square integrable functions. We show that a mean-field equilibrium exists and propose Christine Gruen a fast learning algorithm that converges to mean-field equi- University Toulouse 1- TSE libria. [email protected] Hamidou Tembine Fabien Gensbittel LSS, CNRS-Supelec-Univ. Paris Sud, France University Toulouse 1 -TSE [email protected] 76 CT15 Abstracts

Ousmane Kodio Australian Defence Force Academy Universite de Segou [email protected] [email protected]

CP25 CP24 Convergence of Caratheodory Solutions for Primal- A Variational Approach to Second Order Mean Dual Dynamics in Constrained Concave Optimiza- Field Games with Density Constraints: the Sta- tion tionary Case This paper characterizes the asymptotic convergence prop- In this work we study the existence of solutions of a sta- erties of the primal-dual dynamics to the solutions of a tionary Mean Field Game (MFG) system with a density constrained concave optimization problem using classical constraint on the distribution of the agents. We prove the notions from stability analysis. We motivate our study existence of a solution for both, the subquadratic and the by providing an example which rules out the possibility of superquadratic cases. Our approach is based on the inter- employing the invariance principle for hybrid automata to pretation of the MFG system as the optimality condition analyze the asymptotic convergence. We understand the of the optimal problem of a stationary Fokker-Planck equa- solutions of the primal-dual dynamics in the Caratheodory tion. Using tools from convex analysis and some sharp re- sense and establish their existence, uniqueness, and con- sults in the theory of elliptic equations with measure data, tinuity with respect to the initial conditions. We employ we derive first the optimality system for the qualified prob- the invariance principle for Caratheodory solutions of a lem, i.e. when the Slater condition for the density con- discontinuous dynamical system to show that the primal- straint is satisfied. For non qualified problems, we proceed dual optimizers are globally asymptotically stable under by using an approximation argument. the primal-dual dynamics and that each solution of the dynamics converges to an optimizer. Francisco José Silva Alvarez XLIM, Université de Limoges Ashish Cherukuri Université de Limoges University of California, San Diego [email protected] [email protected]

Alpár Richárd Mészáros Enrique Mallada Universitéd’Orsay California Institute of Technology alpar [email protected] [email protected]

CP25 Jorge Cortes Department of Mechanical and Aerospace Engineering Non-Commutative Least Mean Squares Estimators University of California, San Diego and Coherent Observers for Linear Quantum Sys- [email protected] tems

Quantum versions of control problems are often more difficult than their classical counterparts. To make further CP25 progress, new methods need to be devoloped to estimate Analysis of Uncertain Systems to Compute Their the internal state of plants. In this talk, we consider plants Approximate Models whose internal states are governed by non-commutative linear quantum stochastic differential equations. We obtain Mathematical modelling of practical available systems re- non-commutative least mean squares estimators, and give sulted in higher order models along with the uncertainty conditions which make them physically realizable. Also, within making their study and analysis difficult. As a so- some algorithms for designing coherent quantum observers lution, emerged model order reduction. An effective pro- will be presented. cedure to derive a reduced model for an uncertain systems using Routh approximant is discussed here. The proposed Nina H. Amini methodology is an extension of an existing technique for CNRS Researcher continuous-time uncertain systems. The algorithm is jus- [email protected] tified and strengthened by various available examples from the literature. Zibo Miao, Yu Pan ANU College of Engineering & Computer Science Amit Kumar Choudhary [email protected], [email protected] Indian Insttitute of Technology (Banaras Hindu University) Matthew James Varanasi Faculty of Engineering and Information Technology [email protected] Australian National University [email protected] Shyam Krishna Nagar Dept. of Electrical Engineering Hideo Mabuchi IIT (BHU) Varanasi, U.P. India Applied Physics Department [email protected] Stanford University [email protected] CP25 Shanon L. Vuglar Time Averaged and Spatial Averaged Convergence University of New South Wales, for a Direct Coupled Distributed Coherent Quan- CT15 Abstracts 77

tum Observer [email protected], marco torres @hotmail.com

This presentation considers the convergence properties of a distributed direct coupling quantum observer for a closed CP26 linear quantum system. The proposed distributed observer Extremum Seeking-Based Indirect Adaptive Con- consists of a network of quantum harmonic oscillators and trol for Nonlinear Systems with State-Dependent it is shown that the distributed observer converges in a Uncertainties time averaged sense in which each component of the observer estimates the specified output of the quantum plant. We study in this paper the problem of adaptive trajec- Simulation results also indicate that if the observer is suit- tory tracking for nonlinear systems affine in the control ably constructed then the spatial average of the observer with bounded state-dependent uncertainties. We propose outputs will converge to the plant variable of interest on a to use a modular approach, in the sense that we first de- finite time interval. sign a robust nonlinear state feedback which renders the closed loop input to state stable (ISS) between an esti- Ian Petersen mation error of the uncertain parameters and an output University of New South Wales, tracking error. Next, we complement this robust ISS con- Australian Defence Force Academy troller with a model-free multiparametric extremum seek- [email protected] ing (MES) algorithm to estimate the model uncertainties. The combination of the ISS feedback and the MES algorithm gives an indirect adaptive controller. We show the CP25 efficiency of this approach on a two-link robot manipulator Model Calibration and Control Design in the Pres- example. ence of Model Discrepancy Mouhacine Benosman Measurement and model errors produce uncertainty in Mitsubishi Electric Research Laboratories model parameters estimated through least squares fits to m [email protected] data or Bayesian model calibration techniques. In many cases, model errors or discrepancies are neglected during Meng Xia model calibration. However, this can yield nonphysical University of Notre Dame parameter values for applications in which the effects of [email protected] unmodeled dynamics are significant. It can also produce prediction intervals that are inaccurate in the sense that they do not include the correct percentage of future ob- CP26 servations. In this presentation, we discuss techniques to Tracking Optimal Trajectories in the Restricted quantify model discrepancy terms in a manner that yields Three-Body Problem Using Lqr Feedback physical parameters and correct prediction intervals. We illustrate aspects of the framework in the context of dis- Existing literature has presented optimal trajectories in the tributed structural models with highly nonlinear parameter circular-restricted three-body problem (CRTBP) for ballis- dependencies. Finally, we will discuss the impact of model tic capture and orbit transfers. However, there has been discrepancy and uncertainty quantification on robust con- only a limited discussion thus far of how to stabilize such trol design. trajectories in the presence of noise; e.g. navigation errors, thrust resolution and misalignment. This work ad- Ralph C. Smith dresses stability concerns by introducing an LQR-based North Carolina State Univ feedback strategy that tracks an optimal trajectory in the Dept of Mathematics, CRSC Earth-Moon system. Stability margins are assessed using [email protected] Lyapunov-based methods.

Joseph Dinius CP25 University of Arizona Aircraft Preliminary Design Using Nonlinear In- Program in Applied Mathematics verse Dynamics [email protected]

The question: What shape should an aircraft have to give certain desirable properties? An answer is given by apply- CP26 ing Nonlinear Inverse Dynamics. In general this approach Predicting Time Series Outputs and Time-to- is used to define flight trajectories calculations and flight Failure for An Aircraft Controller Using Bayesian control systems design. Nonlinear model matching is ap- Modeling plied to obtain the preliminary design of aircraft. Given a set of customer flight specifications the parameters which The determination of system stability and time before loss define the shape and size of the required aircraft are deter- of control (time-to-failure) is important for aircraft safety. mined. We describe a hierarchical statistical model using Treed Gaussian Processes to predict stability, time-to-failure, and Daniel L. Mart´ınez output time series. We first classify the data into success CENTRO DE INVESTIGACIN E INNOVACIN and failure, then use separate models for prediction. A EN INGENIERA AERONUTICA basis representation for curves allows us to model variable [email protected] length curves. We demonstrate our prediction method with a neuro-adaptive flight control system. Eduardo Liceaga-Castro, Marco Torres-Reyna Centro de Investigación e Innovación Yuning He en Ingeniera Aeronáutica NASA Ames Research Center 78 CT15 Abstracts

[email protected] controlling many industrial processes. Acknowledgment This research has been co-financed by the European Union (European Social Fund ESF) and Greek national funds CP26 through the Operational Program ”Education and Lifelong Robust Regulation of Siso Systems: The Fractional Learning” of the National Strategic Reference Framework Ideal Approach (NSRF) - Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European So- We solve the robust regulation problem for single-input cial Fund. (ARCHIMEDES III-STRENGHTENING RE- single-output plants by using fractional ideals and with- SERCH GROUPS IN TECHNOLOGICAL EDUCATION, out using coprime factorizations. We are able to formulate NSRF 2007-2015). the famous internal model principle in a form suitable for general factorizations. By using it we are able to give a Michael G. Skarpetis necessary and sufficient solvability condition for the robust Sterea Ellada Institute of Technology regulation problem, which leads to a design method for a Department of Automation Eng. robustly regulating controller. The theory is illustrated by [email protected] examples. Fotis Koumboulis Petteri Laakkonen Sterea Ellada Institute of Technology, Tampere University of Technology Department of Automation Eng. petteri.laakkonen@tut.fi [email protected]

Alban Quadrat Inria Saclay - ˆIle-de-France, Projet DISCO CP27 [email protected] A Decentralized Team Routing Strategy among Telecom Operators in an Energy-Aware Network

CP26 We consider a networking infrastructure, upon which var- The Complexity of Uncertainty in Markov Decision ious “large” users (e.g., Telecom Operators, data centers, Processes etc.) have multiple paths to deliver an aggregated entry flow to a certain destination. The flow of each user can be We consider Markov decision processes with uncertain split among the different paths that traverse energy-aware transition probabilities and two optimization problems in routers. The routers adopt a specific strategy to minimize this context: the finite horizon problem which asks to find the power–delay product for each link, which gives rise to an optimal policy for a finite number of transitions and the quadratic link (in the aggregated link flows) cost functions. percentile optimization problem for a wide class of uncer- We seek person–by–person satisfactory (p.b.p.s.) strate- tain Markov decision processes which asks to find a pol- gies stemming from a team optimal control problem of the icy with the optimal probability to reach a given reward users. The team optimization problem is defined among objective. To the best of our knowledge, unlike other op- Decision Makers (DMs – one for each user) that try to min- timality criteria, the finite horizon problem has not been imize a common aggregate cost function of their routes, considered for the case of bounded-parameter Markov de- each one acting solely on the basis of the knowledge of cision processes, and the percentile optimization problem the amount of flow to be routed. We derive piecewise lin- has only been considered for very special cases. We es- ear p.b.p.s. solutions, which are characterized by a set of tablish NP-hardness results for these problems by showing parameters. The latter can be found by solving a set of appropriate reductions. nonlinear fixed point equations.

Dimitri Scheftelowitsch Franco Davoli TU Dortmund DITEN - University of Genoa [email protected] [email protected]

CP26 Michele Aicardi DIBRIS-University of Genoa Finite Step Algorithms for the Solution of Robust [email protected] Control Problems with Application to Hydraulic and Pneumatic Control Systems Roberto Bruschi In this paper a unification of robust control stabilizabil- CNIT - University of Genoa Research Unit ity algorithms solving many control problems will be pre- [email protected] sented. The convergence of the algorithm is guaranteed under solvability conditions depending upon the particu- Paolo Lago lar robust control problem. A main algorithm with minor DITEN-University of Genoa modifications is presented for solving many robust control [email protected] problems of linear systems with nonlinear uncertain structure, such as robust output asymptotic tracking or robust PID design. The main algorithm is based on the respective CP27 results of Hurwitz invariability (robust stabilizability) of Estimating the Relative Position of Mobile Agents uncertain gained controlled polynomials. The applicability on Jordan Curves from Ambiguous Proximity Data of the proposed algorithms will be illustrated to various hydraulic and pneumatic uncertain systems such as hydraulic We consider the problem of estimating the relative posi- pneumatic actuators, hydraulic motors and pumps. The tions of an ensemble of agents, moving along a Jordan algorithms will be implemented in micro controller based curve. When two of them get sufficiently close, they can platforms and PLC platforms providing a helpful tool for measure their Euclidean distance. Based on the knowl- CT15 Abstracts 79

edge of agent dynamics, a prediction-correction algorithm time-discretization errors and the interpolation ones that described is proposed to recursively estimate the relative are accumulated over time steps. position along the Jordan curve for each pair of agents. Ex- ploiting these position estimates, decentralized formation Yumiharu Nakano control strategy can be implemented on the curve. Graduate School of Innovation Management Tokyo Institute of Technology Franco Garofalo, Piero De Lellis, Francesco Lo Iudice, [email protected] Giovanni Mancini University of Naples Federico II [email protected], [email protected], CP27 [email protected], gio- The Cauchy Attitude Estimator for Planetary [email protected] Flyby in An Intense Radiation Background

There are many estimation problems where both impulsive CP27 measurement and/or process noise occurs. Handling out- An Inversion-Based Fault Reconstruction Ap- liers in the data has been a heuristic process. Recently, proach in Nonlinear Systems a recursive estimator for heavy tailed Cauchy probability density functions that model the measurement and process This paper presents an inversion-based fault reconstruction noise into a discrete-time linear system has been developed. approach for a wide class of nonlinear systems subject to This new scheme directly handles impulsive noise. In fact, an actuator or plant fault. If the nonlinear system has for Cauchy noise, this estimator produces the conditional finite relative order with respect to the fault signal, the mean and is thereby a minimum variance estimator. To inverse system as an observer-based filter, reproduces the demonstrate the improvement that is obtained, this new fault at its output. A simulation for a continuous-stirred estimator is applied to a planetary flyby, where the star- tank reactor (CSTR) model include flow rate fault is used tracker measurements are impulsive due to the electromag- to illustrate the effectiveness of the proposed method. netic radiation characteristics of the planet.

Hamed Kazemi Jason L. Speyer Shahid Beheshti University (SBU) UCLA [email protected] [email protected]

Alireza Yazdizadeh Department of Electrical Engineering CP28 Shahid Abbaspour University Metric Invariance Entropy and Conditionally In- [email protected] variant Measures

Abbas Aliabadi A notion of measure-theoretic invariance entropy is con- MAPNA Group structed with respect to a conditionally invariant measure [email protected] for control systems in discrete time. It is shown that the metric invariance entropy is invariant under conjugacies, the power rule holds, and the (topological) invariance en- CP27 tropy provides an upper bound. Image Compression and Signal Transform Designs Based on Fast and Stable Discrete Cosine and Sine Fritz Colonius Transformation Algorithms University of Augsburg [email protected] Discrete Fourier Transformation is engaged in image processing, signal processing, speech processing, feature extraction, convolution etc. In this talk we elaborate image CP28 compression results based on stable, fast, and recursive Controlling Spatiotemporal Chaos in Active radix-2 Discrete Cosine Transformation (DCT) and Dis- Dissipative-Dispersive Nonlinear Systems crete Sine Transformation (DST) algorithms having sparse and orthogonal factors. We also propose signal transform We develop a novel generic methodology for the sta- designs constructed solely via variants of DCT and DST re- bilization and control of infinite-dimensional dynamical spect to decimation in time and frequency algorithms hav- systems exhibiting low-dimensional spatiotemporal chaos. ing sparse, orthogonal, rotation/rotation-reflection, and The methodology is exemplified with the generalized butterfly matrices. Kuramoto-Sivashinsky equation, the simplest possible prototype that retains that fundamental elements of any non- Sirani M. Perera linear process involving wave evolution. We show that with Daytona State College an appropriate choice of time-dependent feedback controls [email protected] we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, travelling waves and spatiotemporal chaos. We also show that the pro- CP27 posed methodology, appropriately modified, can be used A Collocation Method for Zakai Equations to control the stochastic Kuramoto-Sivashinsky equation and related models. We propose a new numerical method for Zakai equations in nonlinear filtering. The method constructs a numeri- Susana N. Gomes cal solution by the quasi-interpolation in a recursive way. Department of Mathematics We provide the rigorous bound of the approximation er- Imperial College London ror defined by Sobolev norm, which is consisting of the [email protected] 80 CT15 Abstracts

Marc Pradas Ali Al-Maktoumi Department of Mathematical Sciences Sultan Qaboos University, Oman [email protected] Department of Soils, Water and Agricultural Engineering [email protected] Serafim Kalliadasis Department of Chemical Engineering Vitaly Zlotnik Imperial College London University of Nebraska-Lincoln, USA [email protected] Department of Earth and Atmospheric Sciences [email protected] Demetrios Papageorgiou Department of Mathematics Yurii Obnosov Imperial College London, UK Kazan Federal University, Russia [email protected] Institute of Mathematics and Mechanics [email protected] Grigorios Pavliotis Imperial College London Department of Mathematics CP28 [email protected] Subdifferential Inclusions and Tracking Problems The evolution of the state of a system can be usually de- CP28 scribed by a differential inclusion Optimal Control of Passive Particles Advected by x (t) ∈ F (t, x(t)). (2) Two-Dimensional Point Vortices Moreover, in many systems admissible states have to sat- The objective of this work is to develop a mathematical isfy additional viability constraints framework for the modeling, control and optimization of dynamic control systems whose state variable is driven x(t) ∈ K(t)(3) by interacting ODE’s and PDE’s, which should provide a sound basis for the design and control of new advanced en- where K(·) is a family of moving subsets (a tube). In this gineering systems. We are applying necessary conditions of lecture we address a control problem that concerns (2)-(3). optimality to the two-dimensional incompressible Navier- In fact, given an initial state x0, we are interested in finding Stokes flow, which can be reduced to a problem with ODE a control u(t) such that there exits (at least) a solution of dynamics, by using vortex and multiprocess methods, to study the position of a particle subject to this flow. x(t) ∈ u(t)+F (t, x(t)) (4) Teresa D. Grilo x(0) = x0 FCUP/FEUP [email protected] reaching the tube K(·)atafinitetimet∗ and remaining thereafter, that is, such that (3) is satisfied whenever t ≥ S´ılvio Gama t∗. FCUP [email protected] José Alberto Murillo Hernández Departamento de Matemática Aplicada y Estadstica Fernando F. Lobo Pereira Universidad Politécnica de Cartagena Faculadade de Engenharia da Universidade do Porto [email protected] Porto, Portugal fl[email protected] CP28 Swirling Flow Stabilisation and the KdV Equation CP28 Asymptotic analysis of swirling flow through a pipe leads Optimal Control of Managed Aquifer Recharge to the Korteweg de Vries equation. We discuss what this (mar) From Infiltration Trenches With Objec- tells us about the stability of the flow and what it suggests tive of Minimal Waterlogging: Revisiting the about ways to stabilise the flow. Polubarinova-Kochina and Pontryagin Legacy Steve Taylor In MAR, surface water infiltration perturbs water table University of Auckland, New Zealand (moving free boundary). Three phases of transient MAR [email protected] are analytically investigated using Green-Ampts ODE, Boussinesqs linearized PDE and Laplaces PDE with the volume of wetted soil at a specified instance and free sur- MS1 face depth above substratum as criteria. Hydrogeological Dynamic Programming in Mathematical Finance parameters and total annual volume of injected water are constraints. The controls are: time schedule, filling depth- Mathematical Finance has introduced new type of stochas- size-shape of trench, number of trenches. Optimal MAR tic control problems. In this context, the martingale scenarios are found. method has been used to solve them. This gives the im- pression that probabilistic techniques are the only way to Anvar Kacimov obtain a solution. We want to show that purely analytical Sultan Qaboos University techniques can be used for the same result. Not only it [email protected] is useful to have additional techniques, but also analytical CT15 Abstracts 81

techniques allow for more constructive solutions. In par- Centro de Investigacion en Matematicas, Guanajuato, ticular, one does not need to rely on the martingale repre- Mexico sentation theorem to construct optimal stochastic controls. [email protected] We will discuss the concepts and the main techniques. Two models will be considered, the classical consumer-investor model and a model describing the choice of projects for MS1 an entrepreneur. A credit risk problem will be solved in this framework. Do not include references or citations sep- A Measure Approach for Continuous Inventory arately at the end of the abstract. Instead, all citations Models: Long-Term Average Criterion must be in text in the general form [Authorname, Title, etc] This paper examines a single-item inventory process, modelled by a one-dimensional SDE, which incurs long-term Alain Bensoussan average costs. The manager may increase the current in- The University of Texas at Dallas and ventory level but not reduce the inventory level. This paper City University of Hong Kong, Hong Kong provides minimal conditions which imply that an optimal [email protected] ordering policy exists in the class of (s, S) processes. The value is obtained over a restricted class of policies and then shown to be optimal in general. Both linear and nonlinear MS1 optimization is involved. Optimal Control of Piecewise Deterministic Markov Processes Kurt Helmes The main goal of this talk is to study the infinite-horizon Humboldt University of Berlin expected discounted continuous-time optimal control prob- [email protected] lem of piecewise deterministic Markov processes (PDMPs) with the control acting continuously on the jump intensity Richard Stockbridge λ and on the transition measure Q of the process but not University of Wisconsin - Milwaukee on the deterministic flow φ. The set of admissible control [email protected] strategies is assumed to be formed by policies, possibly randomized and depending on the past-history of the process, Chao Zhu taking values in a set valued action space. We provide suf- University of Wisconsin-Milwaukee ficient conditions based on the three local characteristics [email protected] of the process φ, λ, Q, and the semi-continuity properties of the set valued action space, to guarantee the existence and uniqueness of the integro-differential optimality equa- MS2 tion (the so called, Bellman-Hamilton-Jacobi equation) as well as the existence of an optimal (and δ-optimal, as well) Reference Tracking of Depth of Anesthesia Using deterministic stationary control strategy for the problem. Optimal Control Oswaldo Costa Optimal control theory has gained increasing importance in Departamento de Engenharia de Telecomunicacoes e biomedical applications, e.g., in the automatic administra- Contro tion of anesthetics during general anesthesia. One example Escola Politecnica da Universidade de Sao Paulo of a monitored state is the depth of anesthesia, which is [email protected] usually achieved by the joint administration of hypnotics and analgesics. This state is quantified by the bispectral Francois Dufour index (BIS) that varies between 97.7% and 0%. On the Institut de Mathematiques de Bordeaux INRIA Bordeaux other hand, the amount of drug to be administered should Universite Bordeaux 1 be optimized both for patient health and for economical [email protected] reasons. This motivates the use of optimal control in this field of application. In this contribution a static state- Alexey Piunovskiy feedback control law is considered. In order to determine Department of Mathematical Sciences a suitable feedback gain, a nonlinear optimal control prob- University of Liverpool lem (OCP) is formulated and solved using direct methods. [email protected] These methods have become increasingly useful when computing the numerical solution of the OCP. Moreover, they are known to provide a very robust and general approach. MS1 Controlling Lvy Processes by Absolutely Continu- Julaina Almeida, Luis Tiago Paiva ous Processes Universidade do Porto Fac. Engenharia, Portugal Given a spectrally negative Lévy process in the real line, we [email protected], [email protected] consider the problem of controlling its direction (and intensity) using in an additive way absolutely continuous processes, adapted to the information generated by the Lévy Teresa F. Mendonca process. Using the fluctuation theory of processes, it is Universidade do Porto possible to describe the functional that we aim to minimize Faculdade de Ciencias, Departamento de Matemática in terms of the scale function associated with the process, [email protected] and prove that an optimal solution has a refracted form, described in terms of the frontier of some set. Paula Rocha Universidade do Porto Daniel Hernandez-Hernandez Fac. Engenharia, Portugal 82 CT15 Abstracts

[email protected] Germany [email protected], [email protected], [email protected] MS2 Identification of the Fragmentation Role in the Amyloid Assembling Processes and Optimization MS2 of Current Amplification Protocols On the Significance of Singular Controls in Optimal Solutions to Biomedical Problems The goal is to establish a kinetic model of amyloid formation which will take into account the contribution of Optimal control problems for mathematical models of fragmentation to the de novo creation of templating in- biomedical problems often can be described by control- terfaces. We propose a new, more comprehensive math- affine nonlinear systems with an L1-type objective. Typi- ematical model which takes into account previously ne- cally the controls are bounded, for example as dose rates glected phenomena potentially occurring during the tem- or concentrations of therapeutic agents in cancer treat- plating and fragmentation processes. In particular, we try ments or as vaccination rates in epidemiology. In solutions, to capture a potential effect of the topology and geome- bang-bang controls represent administrations of agents at try of prion folding on the elongation and fragmentation full dose with rest periods while singular controls typically properties of a polymer of a given length by separating are time-varying solutions at intermediate and thus lower polymers of the same length into several compartments. than maximum dose values. There exists mounting medi- Additionally, we apply techniques from geometric control cal evidence that ”more is not necessarily better” in can- to the new model to design optimal strategies for accelerat- cer treatments and this has generated significant research ing the current amplification protocols, such as the Protein interest in what could be called the biologically optimal Misfolding Cyclic Amplification (PMCA). dose (BOD). From an optimization perspective, singular controls stand out as the prime candidates in this con- Monique Chyba text. Although in few problems a full synthesis of optimal Dept. of Mathematics controlled trajectories can be established, it becomes of University of Hawaii at Manoa, USA interest, both theoretically and from an application point [email protected] of view, to analyze problems in which singular controls appear as extremals. In this talk, challenges related to Pierre Gabriel finding optimal solutions, like establishing optimality of Université de Versailles St-Quentin-en-Yvelines singular controls, bang-singular junctions and synthesis of France controlled trajectories will be addressed. The connections [email protected] between the types of solutions and medical concepts including metronomic chemotherapy, chemo-switch protocols and Yuri Mileyko adaptive therapy will be discussed. Dept. of Mathematics University of Hawaii at Manoa, Urszula Ledzewicz USA Southern Illinois University, USA [email protected] [email protected]

Jean-Michel Coron Heinz Schaettler Universit´e Pierre et Marie Curie, France Washington University [email protected] [email protected] Rezaei Human Insitut National de la Recherche en Agronomie - INRA, MS3 Protei Minimax Solutions for First Order Mean Field [email protected] Games

We consider first order mean field game system with non- MS2 smooth Hamiltonian enjoying the sublinear growth. Pro- Slow Invariant Manifold Reduced Models for Stiff posed definition of minimax solution means that the graph Chemical Kinetics ODE in Optimal Control of value function is viable under certain differential inclusion, when the measure on the state space is determined Model reduction in the context of numerical optimal con- by a measure on the set of viable trajectories. We prove trol using a multiple shooting approach is a useful way the existence theorem, and the consistency of minimax and to decrease the computational complexity. Mathematical classical solutions. Additionally, we construct a near-Nash models for chemical kinetics based on stiff ordinary differ- equilibrium for finite-player game. ential equations can often be reduced for example by using a trajectory-based optimization approach to compute a Yurii Averboukh slow invariant manifold within the state space. This seems Krasovskii Inst. of Math and Mechanics to be a profitable approach because on the one hand a op- UsB RAS timal control problem has to be solved and on the other [email protected] hand the model reduction is performed via optimization as well. As an example, we discuss the Michaelis-Menten enzyme kintetics in singularly perturbed form and demon- MS3 strate the applicability of our model reduction method for Risk-Sensitive Optimal Control for Mean-Field Dy- singularly perturbed optimal control problems. namics under Partial Observation

Dirk Lebiedz, Pascal F. Heiter,MarcelRehberg We establish a stochastic maximum principle (SMP) for Ulm University control problems of partially observed diﬀusions of mean- CT15 Abstracts 83

ﬁeld type with risk-sensitive performance functionals. [email protected]

Boualem Djehiche Stockholm MS4 [email protected] Optimal Control of the Cahn-Hilliard Variational Inequality Hamidou Tembine LSS, CNRS-Supelec-Univ. Paris Sud, France Abstract not available. [email protected] Michael Hintermüller Department of Mathematics, Humboldt-University of MS3 Berlin [email protected] Mean Field Games: New Results and New Per- spectives MS4 Abstract not available. Optimal Distributed Control of Nonlocal Cahn- Olivier Gueant Hilliard/Navier-Stokes Systems in 2D Université Paris-Diderot UFR de Mathématiques In this talk, we report on joint work with S. Frigeri and E. [email protected] Rocca (both WIAS Berlin). We study the distributed optimal control of nonlocal Cahn-Hilliard/Navier-Stokes systems in the two-dimensional case under box constraints for the controls. The nonlocal contribution to the chemical MS3 potential has the form of a convolution integral with an Mean Field Inspection Games integral kernel having certain smoothness properties; for instance, potentials of Newton or Bessel type are admit- In this talk we present a new model of mean field inspec- ted. Upon showing sufficiently strong regularity and station games with one major player and a large number of bility properties for the solutions to the state system, the inspectees on a discrete state space. Frechet differentiability of the control-to-state mapping in suitable function spaces can be established, and first-order Wei Yang optimality conditions in terms of an adjoint System and a University of Strathclyde variational inequality can be derived. [email protected] Jürgen Sprekels Department of Mathematics, Humboldt-Universität zu Vassili Kolokoltsov Berlin Statistics Dept, University of Warwick [email protected] [email protected]

MS4 MS4 Optimal Control of Electromagnetic Fields Gov- Optimal Control of Phase Field Equations with Dy- erned by the Full Time-Dependent Maxwell Equa- namic Boundary Conditions tions

This talk deals with an optimal control problems for the In this talk, we present recent results in the optimal con- Allen-Cahn equation with a nonlinear dynamic boundary trol of the full time-dependent Maxwell equations. Our condition involving the Laplace-Beltrami operator. The goal is to find an optimal current density and its time- nonlinearities both in the bulk and on the boundary can dependent amplitude which steer the electric and mag- be singular, i.e., they may range from the derivative of log- netic fields to the desired ones. The main difficulty of arithmic potentials confined in [−1, 1] to the subdifferential the optimal control problem arises from the complexity of of the indicator function of the interval [−1, 1] up to a con- the Maxwell equations, featuring a first-order hyperbolic cave perturbation. We first examine the case of logarithmic structure. We present a rigorous mathematical analysis nonlinearities: in a recent paper by Colli and Sprekels the for the optimal control problem. Here, the semigroup the- corresponding control problems were studied, and results ory and the Helmholtz decomposition theory are the key concerning existence and first-order necessary and second- tools in the analysis. Our theoretical findings include ex- order sufficient optimality conditions were shown. Then, in istence, strong regularity, and KKT theory. The corre- the case of double obstacle potentials, a joint research with sponding optimality system consists of forward-backward M. H. Farshbaf-Shaker and J. Sprekels focused on the ”deep Maxwell equations for the optimal electromagnetic and ad- quench” approximation (i.e., approximating the indicator joint fields, magnetostatic saddle point equations for the function by logarithmic nonlinearities) and led us to estab- optimal current density, and a projection formula for the lish both the existence of optimal control and first-order optimal time-dependent amplitude. A semismooth New- necessary optimality conditions. Extensions of these re- ton algorithm in a function space is established for solving sults to the viscous Cahn-Hilliard and Cahn-Hilliard equa- the nonlinear and nonsmooth optimality system. The pa- tion with dynamic boundary condition will be outlined. per is concluded by numerical results, where mixed finite elements and Crank-Nicholson schema are used. Pierluigi Colli Dipartimento di Matematica ”F. Casorati’, Universita’ di Irwin Yousept Pa Fakultät für Mathematik, Universität Duisburg-Essen 84 CT15 Abstracts

[email protected] (PBDW) formulation, a real-time and in-situ data as- similation (state estimation) framework for physical systems modeled by parametrized PDEs. The formulation MS5 addresses anticipated uncertainty through a background Some Results on the Stability of 1-D Nonlinear Hy- (prior) space associated with the parametrized PDE, in- perbolic Systems on a Finite Interval corporates unanticipated uncertainty through a representation update space, identifies stability-informed choices This talk deals with the control of systems modeled by hy- of experimental observations, and incorporates elements of perbolic systems in one space dimension. These systems model reduction to provide real-time computational effi- appear in various real life applications (navigable rivers ciency. We demonstrate the effectiveness of the formula- and irrigation channels, heat exchangers, plug flow chemi- tionusingarealphysicalsystem. cal reactors, gas pipe lines, chromatography,...). On these systems we show methods to construct stabilizing feedback Masayuki Yano,JamesPenn laws. We also show the importance of the choice of func- Massachusetts Institute of Technology tional spaces for the stabilization issue in the nonlinear [email protected], [email protected] case. Tommaso Taddei Jean-Michel Coron MIT Université Pierre et Marie Curie, France [email protected] [email protected] Anthony T. Patera MS5 Massachusetts Institute of Technology Performance Estimates for Model Predictive Con- Department of Mechanical Engineering trol of Pdes [email protected] Model Predictive Control (MPC) is a control technique Yvon Maday which synthesizes an infinite horizon control function from Université Pierre et Marie Curie pieces of finite horizon optimal control functions. It can and Brown university thus be seen as a model reduction technique in time. Often, [email protected] the goal of MPC is to obtain a tracking control steering the system state to a desired reference. In this talk, we explore for various types of PDEs how the cost functional in the MS6 finite horizon PDE optimization in the MPC scheme must Output Regulation for Linear Hybrid Systems with be chosen in order to obtain the desired tracking behaviour Unpredictable Jumps: the Case with Dwell Time and good performance in the sense of an infinite horizon objective. The problem of output regulation for hybrid systems having linear flow and jump maps is considered, under the Lars Grüne assumption that the relevant time domain satisfies a dwell Mathematical Institute time condition but is otherwise unknown. A characteri- Universitaet Bayreuth zation of the steady-state motions achieving regulation is [email protected] provided in terms of hybrid generalizations both of the invariant subspace algorithm and of the Francis equations. Nils Altmüller The two proposed approaches are compared, and relations University of Bayreuth, Germany with the case without dwell time are highlighted. [email protected] Daniele Carnevale Università di Roma ”Tor Vergata” MS5 [email protected] Optimal Control for the Wave Equation: Infinite Versus Finite Horizon Laura Menini, Mario Sassano, Sergio Galeani UniversitàdiRoma We consider a vibrating string that is fixed at one end [email protected], [email protected], with Neumann control action at the other end. We study [email protected] a problem of optimal control where the deviation from the desired state is penalized on the whole time interval and analyze the asymptotic properties as the time horizon tends MS6 to infinity. Due to the structure of the objective function, Stabilization of Switched Affine Systems by Means most of the optimal control action is concentrated at the of State Dependent Switching Laws beginning of the time interval. This presentations addresses the stabilization problem for Martin Gugat a class of switched affine systems. Qualitative conditions Institute of Technology for the existence of stabilizing switching laws dependent on Darmstadt, Germany the systems state will be presented. The proposed method- [email protected] ology is based on the use of an equivalent bilinear model of the original switched system. Furthermore, constructive conditions for local stabilization will presented by emulat- MS5 ing locally classical controllers. The proposed conditions PBDW: Real-Time State Estimation for can be easily reformulated as numerically tractable linear Parametrized PDEs matrix inequalities. We present the parametrized-background data-weak Laurentiu Hetel CT15 Abstracts 85

Ecole Centrale de Lille [email protected] [email protected] Huan Zhang Emmanuel Bernuau The University of Melbourne IRCCyN UMR CNRS 6597 [email protected] [email protected]

MS7 MS6 On Average Control Generating Families for Sin- Geometric Methods for Switching Systems gularly Perturbed Optimal Control Problems

This contribution reviews the basic aspects of the geomet- It is known that, under certain conditions, the dynamics of ric approach to control and regulation problems in linear the slow components of a singularly perturbed (SP) con- switching systems. It is shown that the geometric approach trol system is approximated by solutions of the averaged provides tools and methods for characterizing, in a struc- system, in which the role of controls is played by measure- tural sense, the solvability of non interacting control prob- valued functions. A family of controls and the correspond- lems, as well as of regulation problems, for different classes ing solutions of the fast subsystem is called average control of switching systems. Both the cases in which the switching generating (ACG) if it generates a state-control trajectory signal is measurable and that in which it is not measurable of the averaged system. We will state sufficient and neces- are considered. sary conditions of optimality of ACG families in problems of optimal control considered on the solutions of the av- Anna Maria Perdon eraged system, and we will discuss a linear programming Università Politecnica delle Marche based approach to numerical construction of near optimal [email protected] ACG families. The theoretical results will be illustrated with numerical examples.

MS6 Vladimir Gaitsgory Stability Issues in Disturbance Decoupling for Department of Mathematics Switching Linear Systems Macquarie University Sydney [email protected] Disturbance decoupling – i.e., the problem of making the output insensitive to undesired inputs – is a classical problem of control theory and a main concern in control ap- MS7 plications. Hence, it has been solved for many classes of High-Order Schemes for Stationary Hamilton- dynamical systems, considering both structural and sta- Jacobi-Bellman Equations bility requirements. As to decoupling in linear switching systems, several stability formulations apply. The aim of In this talk we consider stationary Hamilton-Jacobi- this contribution is pointing out different definitions of sta- Bellman equations related to infinite horizon optimal con- bility and devising corresponding synthesis algorithms. trol problems or dynamic games. Our goal is to solve these equations numerically using semi-Lagrangian schemes with Elena Zattoni high-order discretization in space. While for low order dis- University of Bologna cretizations monotonicity ensures convergence of the value [email protected] iteration, i.e., termination of the numerical computation, this is in general no longer the case for high-order methods. Main contribution of the talk is to show how ε- MS7 monotonicity can be used in order to re-establish conver- Max-Plus Fundamental Solution Semigroups for gence and to present a selection of high-order schemes to Optimal Control Problems which this theory applies.

Recent work concerning the development of fundamental Olivier Bokanowski solution semigroups for specific classes of optimal control Université Paris-Diderot and related problems is unified and generalized. By ex- [email protected] ploiting max-plus linearity, semiconvexity, and semigroup properties of the corresponding dynamic programming evo- Maurizio Falcone lution operator, two types of max-plus fundamental solu- UniversitàdiRoma“LaSapienza’,Italy tion semigroup are presented. These semigroups, referred [email protected] to as max-plus primal and max-plus dual space fundamental solution semigroups (respectively), consist of horizon indexed max-plus linear max-plus integral operators. They Roberto Ferretti facilitate the propagation of value functions, and hence the Dipartimento di Matematica e Fisica solution of Hamilton-Jacobi-Bellman equations, to longer UniversitàdiRomaTre time horizons via max-plus convolutions. Their applica- [email protected] tion to specific classes of optimal control problem is also summarised. Lars Grüne Mathematical Institute Peter M. Dower Universitaet Bayreuth The University of Melbourne [email protected] [email protected] Dante Kalise William McEneaney Radon Institute for Computational University of California at San Diego andAppliedMathematics(RICAM) 86 CT15 Abstracts

[email protected] [email protected]

Hasnaa Zidani ENSTA ParisTech, INRIA Saclay MS8 [email protected] Staticization and Associated Hamilton-Jacobi and Riccati Equations

MS7 The use of stationary-action formulations for dynamical systems allows one to generate fundamental solutions for Deterministic Control of Randomly-Terminated classes of two-point boundary-value problems (TPBVPs). Processes One solves for stationary points of the payoff as a function of inputs, a task which is significantly different from We will describe an efficient (noniterative) numerical that in optimal control problems. Both a dynamic pro- method for a class of static HJB problems with free gramming principle (DPP) and a Hamilton-Jacobi partial boundary. Such equations arise in optimal control differential equation (HJ PDE) are obtained for a class of of deterministic-up-to-termination finite-horizon processes, problems subsuming the stationary-action formulation. Al- when the terminal time T is an exponentially distributed though convexity (or concavity) of the payoff may be lost as random variable. A part of this talk will be based on joint one propagates forward, stationary points continue to ex- work with J. Andrews. ist, and one must be able to use the DPP and/or HJ PDE to solve forward to such time horizons. In linear/quadratic Alexander Vladimirsky models, this leads to a requirement for propagation of so- Dept. of Mathematics lutions of differential Riccati equations past finite escape Cornell University times. [email protected] William McEneaney University of California at San Diego MS8 [email protected] Reconstruction of Independent Sub-Domains for a Class of Hamilton-Jacobi Equations and Applica- Peter M. Dower tion to Parallel Computing The University of Melbourne [email protected] A previous knowledge of the domains of dependence of a Hamilton-Jacobi equation can be useful in its study and MS8 approximation. Information of this nature is, in general, difficult to obtain directly from the data of the problem. In On the Use of Non-Stationary Policies for Station- this talk we introduce formally the concept of independent ary Infinite-Horizon Markov Decision Processes sub-domain discussing its main properties and we provide a constructive implicit representation formula. Using such We consider infinite-horizon stationary γ-discounted results we propose an algorithm for the approximation of Markov Decision Processes, for which it is known that these sets that is shown to be relevant in the numerical there exists a stationary optimal policy. Using Value and resolution via parallel computing. Policy Iteration with some error at each iteration, it is well-known that one can compute stationary policies that 2γ Adriano Festa are (1−γ)2 -optimal. After arguing that this guarantee is RICAM tight, we develop variations of Value and Policy Iteration for computing non-stationary policies that can be up to Austrian Academy of Sciences 2γ [email protected] 1−γ -optimal. Boris Lesner, Bruno Scherrer MS8 INRIA [email protected], [email protected] Dynamic Programming for Path-Dependent Deter- ministic Control and Idempotent Expansion Meth- ods MS9 Yield-Analysis of Different Coupling Schemes for It is often seen in control problems that the status of a Interconnected Bio-Reactors system is affected by not only a current state but also a past history of a trajectory. In this presentation, we will Bio-chemical reaction networks are more and more adapted talk about dynamic programming arguments for optimal to be used for the production of fine chemicals. Due to deterministic control under path-dependent dynamics and the appearance of intermediate species which influence the costs. We show that the path-dependent continuous-time single reaction steps, a single compartment approach for value function defined on an infinite-dimensional space can the implementation of such a reaction may not be opti- be approximated by time-discretized path-dependent value mal. Multi-compartment approaches however might have functions which, on the other hand, are given on finite- the potential to increase the yield of desired product if the dimensional spaces. To compute the discrete-time path- coupling of the compartments is chosen appropriately. A dependent value function, we use idempotent expansion model based approach is presented to identify and analyze methods. We will discuss particular cases where idempo- such coupling schemes for a specific enzyme cascade as an tent expansions work. example system.

Hidehiro Kaise Wolfgang Halter Graduate School of Engineering Science University of Stuttgart Osaka University [email protected] CT15 Abstracts 87

Nico Kress ETH Zurich Institute of Technical Biochemistry [email protected], [email protected] Universität Stuttgart [email protected] MS10 Konrad Otte, Sabrina Reich, Bernhard Hauer Impulse Control of Non-Uniformly Ergodic Pro- University of Stuttgart cesses with Average Cost Criterion [email protected], [email protected], We study a problem of impulse control of a Markov process [email protected] that maximises the average cost per unit time criterion: T ∞ 1 x Frank Allgower lim inf E f(Xs)ds − 1τ ≤T c(Xτ −,ξi) , T →∞ i i Universität Stuttgart T 0 i=1 [email protected] where f is a running reward and c ≥ 0 is an impulse cost. We characterise optimal strategies via a solution to an aux- MS9 iliary Bellman equation. The novelty of the paper is a gen- A Simulation-based Approach for Solving Optimi- eral treatment of models in which (Xt) is supported on sation Problems with Steady State Constraints unbounded space and not uniformly ergodic. Our results have applications in balancing of energy systems and in Ordinary differential equations (ODEs) are widely used to managing inventories. Based on a joint work withLukasz model biological, (bio-)chemical and technical processes. Stettner. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. Jan Palczewski This article proposes a simple simulation-based approach University of Leeds for solving optimisation problems with steady state con- [email protected] straints. This simulation-based optimisation method is tailored to the problem structure and exploits the local geom- MS10 etry of the steady state manifold and its stability properties. A parameterisation of the steady state manifold is Ergodic Stopping Problems not required. We prove local convergence of the method The lecture is devoted stopping problems of Markov pro- for locally strictly convex objective functions. Efficiency cesses with functional without discount rate. We show con- and reliability of the proposed method are demonstrated tinuity of the value function and existence of optimal stop- in two examples. ping time. For this purpose we have to impose various ergodic conditions on Markov processes. In general we are Anna Fiedler, Fabian Theis interested in the case when we don’t have uniform ergod- Helmholtz Zentrum München icity. We show the above results under different sets of anna.fi[email protected], assumptions and consider also the case with general dis- [email protected] count rate. The talk is based on a joint paper with J. Palczewski. Jan Hasenauer Helmholtz Zentrum Munchen Lukasz W. Stettner [email protected] Institute of Mathematics [email protected] MS9 A Control Theory for Stochastic Biomolecular Reg- MS10 ulation A Measure Approach for Continuous Inventory Models: Discounted Cost Criterion The tight regulation of the abundance of cellular con- stituents in the noisy environment of the cell is a critical This paper examines a single-item inventory process, mod- requirement for several biotechnology and therapeutic ap- elled by a one-dimensional SDE, which incurs discounted plications. Here we present elements of a new regulation costs. The manager may increase the current inventory theory at the molecular level that accounts for the noisy level but not reduce the inventory level. This paper pro- nature of biochemical reactions and provides tools for the vides very minimal conditions which imply that an optimal analysis and design of robust control circuits at the molec- ordering policy exists in the class of (s, S) processes. The ular level. Using these ideas, we propose a new regulation stochastic problem is imbedded in two different linear pro- motif that implements an integral feedback strategy that grams over a space of measures. The ultimate solution robustly regulates a wide class of reaction networks. Tools relies on duality theory in linear programming. from probability and control theory are then used to show that the proposed control motif preserves the stability of Kurt Helmes the overall network, while steering the population of any Humboldt University of Berlin regulated species to a desired set point. [email protected]

Mustafa Khammash Richard Stockbridge Control Theory and Systems Biology D-BSSE University of Wisconsin - Milwaukee ETH-Z¨urich; 4058 Basel (CH) [email protected] [email protected] Chao Zhu Ankit Gupta, Corentin Briat University of Wisconsin-Milwaukee 88 CT15 Abstracts

[email protected] Faculty of Sciences Meknes [email protected]

MS10 El Hassan Zerrik Representation Formulas for Solutions of Isaacs Universit´e Moulay Ismail - Mekn`es Integro-PDE and Construction of Almost Optimal [email protected] Strategies

We will present sub- and super-optimality inequalities of MS11 dynamic programming for viscosity solutions of Isaacs A Viability Analysis for Structured Model of Fish- integro-PDE associated with two-player, zero-sum stochas- ing Problem tic differential game driven by a Lévy type noise. This implies that the lower and upper value functions of the In this work we study a structured fishing model, basi- game satisfy the dynamic programming principle and they cally displaying the two stages of the ages of a fish pop- are the unique viscosity solutions of the lower and up- ulation, which are in our case juvenile, and adults. We per Isaacs integro-PDE. Our method uses PDE techniques associate to this model two constraints: one of ecological and is based on regularization of viscosity sub- and super- type ensuring a minimum stock level, the other one of eco- solutions of Isaacs equations to smooth sub- and super- nomic type ensuring a minimum income for fishermen. The solutions of slightly slightly perturbed equations, and ap- analytical study focuses on the compatibility between the proximate optimal synthesis. It is constructive and pro- state constraints and the controlled dynamics. Using the vides a fairly explicit way to produce almost optimal con- mathematical concept of viability kernel, we define a set of trols and strategies. constraints combining the guarantee of consumption and a stock of resources to be preserved at all times. Shigeaki KOike Tohoku University Mounir Jerry [email protected] UniversitéIbnTofa¨ıl [email protected] Andrzej J. Swiech Georgia Tech Chakib Jerry Department of Mathematics Equipe EIMA, Departement de Mathematiques [email protected] Faculty of Sciences [email protected] MS11 Viability Radius and Robustness for a class of Lin- MS11 ear Systems A Viability Analysis of Fishery Controlled by In- We consider the problem of robust viability and viability vestment Rate radius for a class of linear disturbed systems. The problem consists in the determination of the smallest disturbance This work presents a stock/effort model describing both harvested fish population and fishing effort dynamics. The f, for which a given viable state z0 do not remains viable. We also consider the problem of the determination of the fishing effort dynamic is controlled by investment which f corresponds to the revenue proportion generated by the smallest disturbance f for which the viability set ViabK activity. The dynamics are subject to a set of economic is empty, which we call the Minimal Lethal Disturbance and biological state constraints. The analytical study fo- (MLD). This work is motivated by the problem of Minimal cuses on the compatibility between state constraints and Lethal Dose in toxicology. controlled dynamics. By using the mathematical concept Abdes Samed Bernoussi of viability kernel, we reveal situations and management Faculty of Sciences and Techniques, tangier, Morocco options that guarantee a sustainable system. [email protected] Nadia Raissi Faculty of Sciences Rabat Mina Amharref, Mustapha Ouardouz [email protected] FST, Tangier [email protected], [email protected] C Sanogo Ibn Tofail University, Faculty of Sciences MS11 [email protected] Constrained Optimal Control of Bilinear Systems: Application to An HVAC System Slimane Benmiled Université de Tunis-El Manar Institut Pasteur de Tunis We investigate the constrained optimal control problem [email protected] of bilinear systems. We minimize a quadratic cost functional over a set of admissible controls given by Uad = 2 m {u ∈ L (0,T,R ):umin ≤ u ≤ umax and α ≤ MS12 v, uL2(0,T,Rm) ≤ β}, using functional analysis tools. We Dynamic Programming Using Radial Basis Func- develop algorithms that allow to compute the optimal con- tions trol, and we apply our approach to an HVAC (Heating Ventilating and Air Conditioning) system, where the total We propose a discretization of the time-discrete Hamilton- consumed energy must not exceed a given ceiling. Jacobi-Bellman equation in optimal control in space by radial basis functions in combination with a moving least Nihale El Boukhari squares projection type operator (aka ’Shepards method’). CT15 Abstracts 89

We show convergence of the associated fixed point itera- Localization and Planning tion, demonstrate the simplicity of the implementation by a corresponding Matlab code and present several numerical In this talk, I will provide an overview of some recent work experiments from optimal control. on localization and planning for mobile agents in a unknown/partially known environment using qualitative in- Oliver Junge formation abstracted from dense metric data. By modeling Center for Mathematics the problem from a topological perspective and using re- Technische Universitaet Muenchen, Germany cent advances in the area of algebraic topology, we will [email protected] derive methods for localization as well as planning strategies. Alex Schreiber Center for Mathematics Alberto Speranzon Technische Universität München United Technologies Research Center [email protected] [email protected]

MS12 MS13 A Spectral Assignment Approach for the Graph Discrete-time Control for Systems of Interacting Isomorphism Problem Objects with Unknown Random Disturbance Dis- tributions: A Mean Field Approach In this presentation, we will propose a heuristic for the We are concerned with stochastic control systems com- graph isomorphism problem that is based on the eigen- posed of a large number N of interacting objects sharing decomposition of the adjacency matrices. If the graphs a common environment. The dynamic of each object is possess repeated eigenvalues, which typically correspond determined by a stochastic difference equation, where the to graph symmetries, finding isomorphisms is challenging. random disturbance density is unknown to the controller. By repeatedly perturbing the adjacency matrices, it is pos- The system is modeled as a Markov control process and is sible to break symmetries of the graphs without changing the isomorphism. This heuristic approach can be used to analyzed according to the mean field theory. Then, combining the mean field limit with a suitable statistical esti- construct a permutation which transforms GA into GB . mation method of the density, we construct control policies Stefan Klus which are nearly asymptotically optimal for the N-system, Freie Universitat Berlin under a discounted optimality criterion. [email protected] J. Adolfo Minjarez-Sosa, Carmen Higuera-Chan Departamento de Matemáticas, Universidad de Sonora Tuhin Sahai [email protected], carg [email protected] United Technologies [email protected] Hector Jasso-Fuentes CINVESTAV-IPN MS12 [email protected] Graphical Model Based Representation of Dynam- ical Systems MS13 Bayesian Networks are widely used to characterize the Stationary Almost Markov Perfect Equilibria in joint dependence between random variables in multivari- Discounted Stochastic Games ate problems due to their compactness and availability of We study discounted stochastic games with Borel state efficient learning/ inference algorithms. This talk high- and compact action spaces depending on the state vari- lights the incorporation of deterministic relations, which able. The transition probability is a convex combination may either be learned or explicitly embedded, within the of finitely many probability measures depending on states framework of Bayesian networks to improve model fidelity and it is dominated by some finite measure on the state while reducing complexity. Further, we motivate the need space. Our main result establishes the existence of sub- of this work by presenting concrete practical examples from game perfect equilibria, which are stationary (the equilib- engineering domain. rium strategy is determined by a single function of the current and previous states of the game). Kushal Mukherjee, Blanca Florentino Liano United Technologies Research Center - Ireland Andrzej Nowak [email protected], fl[email protected] University of Zielona Gora [email protected] Ashutosh Tewari ExxonMobil Research & Engineering Company Anna Jaskiewicz Annandale, New Jersey Institute of Mathematics and Computer Science [email protected] Wroclaw University of Technology [email protected] Anarta Ghosh United Technologies Research Center - Ireland [email protected] MS13 On Risk Processes Controlled by Investment and Reinsurance MS12 From Geometry to Topology in Mobile Robotics: This contribution investigates insurance models for which 90 CT15 Abstracts

the risk/reserve process can be controlled by reinsurance [email protected] and investment in the financial market. Assuming that the company can control its wealth process over time in two different ways: the reinsurance level and the amount MS14 of capital invested in the risky asset, the main objectives of these works are to search the probability that the com- Budget-Constrained Infinite Horizon Optimal Con- pany eventually becomes insolvent. A recent innovative trol Problem approach uses continuous time Semi-Markov processes to unify the time of events that produce changes in the risk In this talk a class of infinite horizon optimal control prob- process, say claim arrivals and price changes of the risky lems with an isoperimetric constraint, also interpreted as asset. Additional capital injection elements may be consid- a budget constraint, is considered. The problem setting ered by the company in order to maintain its wealth over includes a weighted Sobolev space as the state space. We a desired level. The finite horizon problem is faced and investigate the question of existence of an optimal solution partial solutions are presented. and establish a Pontryagins Type Maximum Principle as a necessary optimality condition including a transversal- Rosario Romera ity condition. Which influence the isoperimetric constraint Statistics Dept, Univ. Carlos III de Madrid may have on the feasible set and on the existence of an [email protected] optimal solution is illustrated in details on examples.

MS13 Valeriya Lykina, Sabine Pickenhain On the Vanishing Discount Factor Approach for Brandenburg University of Technology Cottbus, Germany Markov Decision Processes with Weakly Continu- [email protected], sabine.pickenhain@tu- ous Transition Probabilities cottbus.de

This note deals with average cost Markov decision processes with Borel state and control spaces, possibly un- MS14 bounded costs and non-compact action subsets, and weak continuous transition law. Based on recent results of Optimal Control of Epidemiological Seir Models Feinberg, Kasyanov and Zadoianchuk (MOR 37, 591-607, with L1-Objectives and Control-State Constraints 2012), this note provides an elementary proof of the existence of average cost optimal stationary policies using the Optimal control is an important tool to determine vacci- vanishing discount factor approach. nation policies for infectious diseases. For diseases transmitted horizontally, SEIR compartment models have been Oscar Vega-Amaya used. Most of the literature on SEIR models deals with Departamento de Matemáticas cost functions that are quadratic with respect to the con- Universidad de Sonora, México trol variable, the rate of vaccination. In this paper, we con- [email protected] sider L1-type objectives that are linear with respect to the control variable. Various pure control, mixed control–state and pure state constraints are imposed. For all constraints, MS14 we discuss the necessary optimality conditions of the Max- Non-degenerate Forms of the Extended Euler- imum Principle and determine optimal control strategies Lagrange Condition for State Constrained Optimal that satisfy the necessary optimality conditions with high Control Problems accuracy. Since the control variable appears linearly in the Hamiltonian, the optimal control is a concatenation We consider state constrained optimal control problems in of bang-bang arcs, singular arcs and boundary arcs. For which the dynamic is represented in terms of a differen- pure bang-bang controls, we are able to check second-order tial inclusion, and the state and the end-point constraints sufficient conditions. are closed sets. We shall discuss simple examples which illustrate how the interplay among the state constraint, the left-end point constraint and the velocity set might influ- Maria d Rosario de Pinho ence the possibility to apply the necessary conditions for Faculdade de Engenharia da Universidade do Porto optimality in the non-degenerate form. We show that this DEEC is actually a common feature for general state constrained [email protected] optimal control problems. Helmut Maurer Piernicola Bettiol, Nathalie Khalil Universität Münster Université de Bretagne Occidentale Institut für Numerische und Angewandte Mathematik Brest, France [email protected] [email protected], nathalie.khalil@univ- brest.fr MS15 MS14 Robust Mean-Field Games to Model Emulation in Analytical Study of Optimal Control Intervention Opinion Dynamics Strategies for Ebola Epidemic Model Abstract not available. Abstract not available.

Ellina V. Grigorieva Dario Bauso Texas Woman’s University Dept of Chemical Engineering Department of mathematics and computer sciences University of Padova CT15 Abstracts 91

[email protected] of the models.

Lubomir Banas MS15 Department of Mathematics, Bielefeld University [email protected] Monotonicity Methods for Mean-Field Games

Abstract not available. MS16 Diogo Gomes Model Predictive Control of Two-Phase Flow Us- King Abdullah Univeristy of Science and Technology ing a Diffuse-Interface Approach [email protected] We present a nonlinear model predictive control framework for closed-loop control of two-phase flows. The fluid is modeled by a thermodynamically consistent diffuse interface MS15 model proposed in [H. Abels, H. Garcke, G. Grün, Thermo- Continuous Time Mean Field Consumption- dynamically consistent, frame indifferent diffuse interface Accumulation Modeling models for incompressible two-phase flows with different densities, M3AN, 22(3), 2012] and allows for fluids of dif- We consider continuous time mean field consumption- ferent densities and viscosities. We adapt the concept of in- accumulation games. The capital stock evolution of each stantaneous control to construct finite dimensional closed- agent is based on the Cobb-Douglas production function loop control strategies for two-phase flows. We provide and takes into account stochastic depreciation. The indi- numerical investigations which indicate that finite dimen- vidual HARA-type utility depends on both the own con- sional instantaneous control is well suited to stabilize two- sumption and relative consumption. We analyze the fixed phase flows. point problem of the mean field game. The individual strategy is obtained as a linear feedback with the gain re- Michael Hinze flecting the collective behaviour of the population. Universität Hamburg Department Mathematik Minyi Huang [email protected] Carleton University School of Mathematics and Statistics Christian Kahle [email protected] University of Hamburg [email protected] Son L. Nguyen Carleton University [email protected] MS16 Drag Optimisation in a Stationary Navier-Stokes Flow Using a Phase Field Approach MS15 The Evolutionary Game of Pressure and Resistance We present a phase field formulation for boundary objective functionals in shape optimisation with stationary We extend the framework of evolutionary inspection game Navier-Stokes flow. With an additional Ginburg-Landau (put forward recently by the authors and his co-workers) regularisation, we prove existence of a minimiser and de- to a large class of conflict interactions between a major rive first order necessary optimality conditions for a general player and a large group of small players. The results are functional. The same results can be deduced for the drag applied to the analysis of the processes of inspection, cor- functional, and via a formal asymptotic analysis, we show ruption, cyber-security, counter-terrorism, epidemiology, that the sharp interface description of the drag optimisa- interaction of humans with their environment and many tion problem can be recovered from the phase field model. other. The contribution will develop the ideas expressed Kei-Fong Lam in the author’s preprint ’The evolutionary game of pres- Universität Regensburg, Fakultät für Mathematik sure (or interference), resistance and collaboration’ (2014), [email protected] http://arxiv.org/abs/1412.1269

Vassili Kolokoltsov MS16 Statistics Dept, University of Warwick [email protected] Optimal Control of a Semidiscrete Cahn- Hilliard/Navier-Stokes System with Variable Densities MS16 In this talk we consider a time discretization of the Cahn- Numerics and Optimal Control for Phase-Field Hilliard/Navier-Stokes system with variable densities by Models of Multiphase Flow Abels-Garcke-Grün and study an associated optimal control problem. It focus is on the non-smooth double-obstacle Flow of mixtures of incompressible fluids with complex potential and distributed control action. Existence of min- fluid interactions (surface tensions, contact angles) can be imizers are shown and first-order optimality conditions are described by a system of (multicomponent) Cahn-Hilliard- derived by a Yosida type approximation. The resulting sta- Navier-Stokes equations. We propose finite element based tionarity system corresponds to a function space version of numerical approximations of non-smooth phase-field mod- C-stationarity. els for mixtures of incompressible fluids with variable densities and viscosities. We discuss theoretical and practical Michael Hintermüller issues related to the proposed numerical approximations. Department of Mathematics, Humboldt-University of We also discuss numerical approaches for optimal control Berlin 92 CT15 Abstracts

[email protected] and convergence theory.

Tobias Keil, Donat Wegner Weiwei Hu Humboldt University of Berlin University of Southern California [email protected], [email protected] [email protected]

John Singler MS17 Missouri S&T Mathematics and Statistics Feedback Control of Vortex Shedding Using Inter- [email protected] polatory Model Reduction

We demonstrate the linear feedback control of vortex shed- MS17 ding in flows with one or two circular cylinders where Reduced-Order Surrogate Models for Closed-Loop rotation is used as the actuation mechanism. Reduced- Control order models of the linearized system are computed using interpolatory model reduction and the computed feed- A stabilizing feedback control is computed for a semilin- back control laws are shown to be effective in stabiliz- ear parabolic PDE utilizing a nonlinear model predictive ing both steady-state and time-averaged flows for low- (NMPC) method. In each level of the NMPC algorithm Reynolds number flows. The feedback control designs are the finite time horizon open loop problem is solved by a also used to determine the effective placement of sensors. reduced-order strategy based on proper orthogonal decomposition. A stability analysis is derived for the combined Jeff Borggaard, Serkan Gugercin algorithm so that the lengths of the finite time horizons Virginia Tech are chosen in order to ensure the asymptotic stability of Department of Mathematics the computed feedback controls. [email protected], [email protected] Stefan Volkwein Universität Konstanz MS17 Department of Mathematics and Statistics Model Reduction Based Feedback Control of the [email protected] Monodomain Equations Alessandro Alla Optimal control of reaction-diffusion systems arising in Department of Mathematics electric cardiophysiology has become an important research University of Hamburg, Germany topic. The monodomain equations represent a reasonably [email protected] accurate model for the electric potential of the human heart. In view of terminating cardiac arrhythmia, feed- Maurizio Falcone back methodologies are of particular interest. In this talk, Università di Roma “La Sapienza’, Italy it is shown that the PDE-ODE structure of the linearized [email protected] monodomain equations leads to a system that is not null controllable but that can still be stabilized by finite dimensional controllers. This allows for constructing the con- MS18 troller based on model reduction techniques. While the Gamkrelidze-Like Maximum Principle for Optimal reduced model is obtained from the linearized system, it Control Problems with State Constraints is shown that it locally stabilizes the nonlinear system as well. This report addresses necessary conditions of optimality for optimal control problem with state constraints in the Tobias Breiten form of the Pontryagin’s Maximum Principle (MP). For University of Graz such problems, these conditions were first obtained by R.V. [email protected] Gamkrelidze in 1959 and subsequently published in the classic monograph by the four authors. His MP was ob- Karl Kunisch tained under a certain regularity assumption on the opti- Karl-Franzens University Graz mal trajectory. Somewhat later, in 1963, A.Ya. Dubovit- Institute of Mathematics and Scientific Computing skii and A.A. Milyutin proved another MP for problems [email protected] with state constraints. In contrast with the MP of R.V. Gamkrelidze, this MP was obtained without a priori regularity assumptions, and, thereby, it degenerates in many MS17 cases of interest. Later, under an additional assumption of controllability of the optimal trajectory, other versions of Balanced POD Model Reduction for Parabolic the MP have been obtained so that they no longer degen- PDE Systems with Unbounded Input and Output erate. Here, we suggest a MP in a form close to the one Operators proposed by R.V. Gamkrelidze but without any a priori regularity assumptions on the optimal trajectory. However, Balanced POD is a data-based model reduction algorithm the absence of regularity assumptions does not ensure the that has been widely used for linearized fluid flows and nondegeneracy of this MP. Therefore, we prove that, under other linear parabolic PDE systems with inputs and out- certain additional conditions of controllability relatively to puts. We consider balanced POD algorithms for such sys- the state constraints at the end-points, or regularity of the tems when the input and output operators are unbounded, reference control process, degeneracy will not occur, since as can occur when control actuators and sensors are located an appropriate non-triviality condition will be satisfied. on the boundary of the physical domain. We discuss computational challenges, standard and modified algorithms, Aram Arutyunov CT15 Abstracts 93

Moscow State University function is demonstrated without any convexity assump- [email protected] tion.

Dmitry Karamzin Nobusumi Sagara Computing Centre of the Russian Academy of Sciences Department of Economics dmitry [email protected] Hosei University [email protected] Fernando L. Pereira Porto University Boris Mordukhovich fl[email protected] Department of Mathematics, Wayne State University [email protected] MS18 Pontryagin Principle in Infinite-Dimensional MS19 Discrete-Times Problems A Cubature Based Algorithm to Solve Decoupled McKean-Vlasov Forward-Backward SDEs We present Pontryagin principle in infinite-dimensional infinite-horizon discrete-times optimal control for systems As shown by Carmona, Delarue and Lachapelle (2012), which are governed by difference equations or by difference the solution of a Mean-Field Game problem (and also the inequations. We use techniques of optimization in Banach one of the related optimization of McKean-Vlasov type dy- ordered spaces. namics problem) is linked to a system of forwardbackward stochastic differential equations with coefficients depend- Mohammed Bachir ing on the marginal distributions of the solutions. We UniversitéParis1 call those types of equations McKean Vlasov Forward- [email protected] Backward SDEs (MKV-FBSDE). In this talk, I will introduce an algorithm to solve decoupled MKV-FBSDEs, which appear in some stochastic control problems in a MS18 mean field environment. We will start by defining a de- The Euler Lagrange Equation and the Regularity terministic algorithm to approximate weakly a MKV- For- of Solutions to Variational Problems ward SDE, as an alternative to the usual approximation methods based on interacting particles. The algorithm In this talk we will consider the problem of minimizing is based on the cubature method of Lyons and Victoir (2004), and given enough regularity of the coefficients of the equation, it can be parametrized to obtain any given [L(∇v(x)) + g(x, v(x))]dx Ω order of convergence. Then, we show how to construct im- plementable algorithms to solve decoupled MKV-FBSDEs. We give two algorithms and show that they have conver- ∈ 0 1,1 with boundary conditions v u + W (Ω) and, assuming gence of order one and two under appropriate regularity asolutionu to exist, we will focus on the problem of the va- conditions. Finally, we proceed to illustrate our results by lidity of the Euler-Lagrange equation for the solution and means of some numerical examples. This is a joint work on the main application of this equation, namely to prove with P.E. Chaudru de Raynal the regularity of the solution itself. We will present an overview of the state of the art with respect to the valid- Camilo A. Garcia Trillos ity of the Euler-Lagrange equation, as well as some recent University College London, results and some open problems. We shall then consider UK the problem of the regularity of the solution: we mini- [email protected] mize an integral functional over a space of functions having first order weak derivatives and, under some reasonable conditions, it turns out the the solution has second order MS19 derivatives. We shall try to clarify the mechanism of this ”Phase Diagram” of a Simple Mean Field Game phenomenon and present some recent results in this direction. We present a detailed analysis about a simple mean field game model called “the seminar problem’ after [O. Gueant, Arrigo Cellina J.-M. Lasry and P.-L. Lions, 2010]. This model is charac- Universita degli Studi di Milano-Bicocca terized by the fact that every agent optimizes his trajectory [email protected] with respect to a simple random event (the seminar starting time) which derives from the collective behavior. In the mean field limit, this event becomes deterministic and MS18 a rather thorough understanding of the solutions can be Subdifferentials of Nonconvex Integral Functionals achieved. In particular, for a sensible class of initial con- in Banach Spaces: A Gelfand Integral Representa- ditions, distinct behaviors can be associated to different tion domains of the parameter space.

We investigate subdifferential calculus for integral func- Thierry Gobron tionals on nonseparable Banach spaces. To this end, we Université de Cergy-Pontoise, France present a new approach in which the Clarke and Mor- [email protected] dukhovich subdifferentials of an integral functional are re- graded as a Gelfand integral of the subdifferential mapping Denis Ullmo of an integrand. Main results are applied to stochastic DP Laboratoire de physique théorique et modèles statistiques with discrete time, and the differentiability of the value CNRS Université Paris-Sud,Orsay, France 94 CT15 Abstracts

[email protected] best response strategy to the mean of the state and the mean-ﬁeld equilibrium, are provided. Igor Swiecicki LPTM, Universit´e de Cergy Pontoise & Hamidou Tembine [email protected] LSS, CNRS-Supelec-Univ. Paris Sud, France [email protected]

MS19 Boualem Djehiche Mean Field Games Equilibrium in a SIR Vaccina- Stockholm tion Model [email protected]

Recent debates concerning the innocuity of vaccines with respect to the risk of the epidemic itself lead to vaccination MS20 campaign failures. We analyze, in a SIR model, whether Long and Winding Central Paths individuals driven by self interest can reach an equilibrium with the society. We show, in a Mean Field Games context, We disprove a continuous analog of the Hirsch conjecture that an equilibrium exists and discuss the price of anarchy. proposed by Deza, Terlaky and Zinchenko, by construct- Finally, we apply the theory to the 2009-2010 Inﬂuenza A ing a family of linear programs with 3r + 4 inequalities in (H1N1) vaccination campaign in France. dimension 2r + 2 where the central path has a total curvature in Ω(2r/r). Our method is to tropicalize the central Laetitia Laguzet path in linear programming. The tropical central path is Universit´e Paris-Dauphine the piecewise-linear limit of the central paths of parameter- [email protected] ized families of linear programs viewed through logarithmic glasses.

MS19 Xavier Allamigeon CMAP, Ecole Polytechnique Fokker-Planck Optimal Control Problems [email protected] The Fokker-Planck (FP) equations are partial differential equations describing the time evolution of the probabil- Pascal Benchimol ity density function (PDF) of stochastic processes. These EDF R&D, Département OSIRIS equations are of parabolic type corresponding to the PDF [email protected] of It¯o processes, and of hyperbolic type for the PDF of piecewise deterministic processes. For FP equations Stephane Gaubert on bounded domains, we investigate the Chang-Cooper INRIA and CMAP, Ecole Polytechnique scheme for space discretization and first- and second-order [email protected] backward time differencing. We prove that the resulting space-time discretization schemes are accurate, condition- Michael Joswig ally stable, conservative, and positivity-preserving. For Technische Universität Berlin the case of unbounded domains, the Hermite spectral dis- [email protected] cretization method is applied and analyzed as well. Next, two optimal control formulations based on the FP equations are discussed in order to control the corresponding MS20 PDFs. To approximate the solutions, the Hermite spectral A Max-Plus Fundamental Solution Semigroup for discretization method is applied. Within the framework of a Class of Lossless Wave Equations Hermite discretization, we obtain sparse-band systems of ordinary differential equations. We analyze the accuracy of A new max-plus fundamental solution semigroup is pre- the discretization schemes by showing spectral convergence sented for a class of lossless wave equations. This new in approximating the state, the adjoint, and the control semigroup is developed via formulation of the action prin- variables that appear in the FP optimality systems. ciple as an optimal control problem for the wave equations of interest, followed by the construction of a max-plus fun- Masoumeh Mohammadi damental solution semigroup for this optimal control prob- Institut für Mathematik, lem using dynamic programming. An application of this Universität Würzburg semigroup to solving two-point boundary value problems [email protected] is discussed via an example.

Peter M. Dower MS19 The University of Melbourne On the Solvability of Risk-Sensitive Linear- [email protected] Quadratic Mean-Field-Type Teams and Games William McEneaney In this paper, we formulate and solve mean-field-type team University of California at San Diego and game problems described by a linear stochastic dynam- [email protected] ics of McKean-Vlasov type and a quadratic or exponential- quadratic cost functional for each player. The optimal strategies of the players are given explicitly using a sim- MS20 ple and direct method based on square completion and a Tropicalizing Semialgebraic Pivoting Rules, Or Girsanov-type change of measure. This approach does not How to Solve Mean Payoff Games in Polynomial use the well-known solution methods such as the Stochastic Time on Average Maximum Principle and the Dynamic Programming Prin- ciple. Sufficient conditions for existence and uniqueness of We introduce an algorithm which solves mean payoff games CT15 Abstracts 95

in polynomial time on average, assuming the distribution Dept of Math & Ctr for Rsch in of the games satisfies a flip invariance property on the set [email protected] of actions associated with every state. The algorithm is a tropical analogue of the shadow-vertex simplex algorithm, which solves mean payoff games via linear feasibility prob- MS21 lems over the tropical semiring. The proof relies on the Sensitivity Analysis and Control in the Lamina observation that certain semi-algebraic pivoting rules can Cribrosa be tropicalized. We discuss sensitivity analysis with respect to important Xavier Allamigeon biological parameters (Lame coefficients, intra-ocular pres- CMAP, Ecole Polytechnique sure and retrolaminar tissue pressure) for a poroelastic [email protected] model describing the lamina cribrosa in the eye. It is be- lieved that the biomechanics of the lamina cribrosa plays Pascal Benchimol an important role in the retinal ganglion cell loss in glau- EDF R&D, Département OSIRIS coma. Our goal is to reveal which parameters are most [email protected] influential and need to be controlled in order to prevent the development of glaucoma. Stephane Gaubert INRIA and CMAP, Ecole Polytechnique Lorena Bociu [email protected] N. C. State University Raleigh, NC [email protected] MS20 On the Regulation Problem for Tropical Linear Event Invariant Dynamical Systems MS21 Approximation Methods for Feedback Stabilization Tropical linear event-invariant systems describe the firing of Boussinesq Equations dynamics for timed event graphs with fixed times. In this context, the regulation problem can be defined as the prob- Pure Dirichlet boundary control of thermal fluids systems lem of controlling the inputs so a given specification, de- leads to technical issues of control compatibility for 3D scribed by a semimodule, is achieved. It will be shown that, problems. In this paper we replace the pure Dirichlet under some technical assumptions, this regulation problem problem with an approximating Robin boundary condition can be reduced to a two-sided eigenproblem, which in turn which eliminates the compatibility condition. We show can be solved using parametric mean payoff games. the resulting Neumann/Robin boundary control problem is well posed and can be used to locally exponential stabi- Vinicius Goncalves lize the Boussinesq equations. Numerical results are given Unveristy Federal Minas Gerais to illustrate the method and convergence of the approxi- [email protected] mation scheme.

Laurent Hardouin John A. Burns ISTIA / LISA - Angers University Virginia Tech [email protected] Interdisciplinary Center for Applied Mathematics [email protected] Carlos Andrey Maia University Federal Minas Gerais, Belo Horizonte Brazil [email protected] MS21 Control of the Cardiovascular-Respiratory System under External Perturbations MS21 Modeling and Estimation in Control of Immune Exploiting the fact that in the combined cardiovascular- Response to BK Virus Infection and Donor Kid- respiratory system the partial pressure of CO2 in arterial ney in Renal Transplant Recipients bloodisregulatedto40mmHgwepresentresultsonthe reaction of the system to external perturbations using the In this presentation we discuss the feedback control prob- Euler-Lagrange formulation of the corresponding optimal lem that results from the involuntary immune-suppression control problem. Numerical issues concerning stiﬀness of that is a standard therapy for organ transplant patients. the resulting two-point boundary value problem will be We develop and validate with bootstrapping techniques discussed. a mechanistic mathematical model of immune response to both BK virus infection and a donor kidney based on Doris H. Fuertinger known and hypothesized mechanisms in the literature. The Renal Research Institute New York model presented does not capture all the details of the im- [email protected] mune response but possesses key features that describe a very complex immunological process. We then estimate Franz Kappel model parameters using a least squares approach with a Department of Mathematics and Scientiﬁc Computing typical set of available clinical data. Sensitivity analysis University of Graz combined with asymptotic theory is used to determine the [email protected] number of parameters that can be reliably estimated given the limited number of observations. H. Thomas Banks MS22 North Carolina State Univ Lookback Option Pricing for Regime-Switching 96 CT15 Abstracts

Jump Diffusion Models George Yin Wayne State University We will introduce a numerical method to price the Euro- Department of Mathematics pean lookback floating strike put options where the un- [email protected] derlying asset price is modeled by a generalized regime- switching jump diffusion process. In the Markov regime- switching model, the option value is a solution of a coupled MS22 system of nonlinear integro-differential partial differential An Optimal Mean-Reversion Trading Rule under equations. Due to the complexity of regime-switching a Markov Chain Model model, the jump process involved, and the nonlinearity, closed-form solutions are virtually impossible to obtain. This paper is concerned with a mean-reversion trading We use Markov chain approximation techniques to con- rule.In contrast to most market models treated in the liter- struct a discrete-time Markov chain to approximate the op- ature, the underlying market is solely determined by a two- tion value. Convergence of the approximation algorithms state Markov chain. The major advantage of such Markov is proved. Examples are presented to demonstrate the ap- chain model is its striking simplicity and yet its capability plicability of the numerical methods. of capturing various market movements. The purpose of this paper is to study an optimal trading rule under such a Zhuo Jin model. The objective of the problem under consideration is University of Melbourne, Australia to find a sequence stopping (buying and selling) times so as [email protected] to maximize an expected return. Under some suitable conditions, explicit solutions to the associated HJB equations Linyi Qian (variational inequalities) are obtained. The optimal stop- East China Normal University ping times are given in terms of a set of threshold levels. A [email protected] verification theorem is provided to justify their optimality. Finally, a numerical example is provided to illustrate the results. MS22 Qing Zhang Approximation of Basket CDS Price on Default University of Georgia Sensitive Regime Switching Model Department of Mathematics [email protected] In this work, we derive the sufficient conditions for the convergence of the approximation of the basket CDS price via the weak convergence method. Particularly, the volatility MS23 of the underlying risk neutral price switches among finite Lmi Formulation of Analysis and Control Problems many regimes driven by the default events occurred in the Involving Fractional Order Models past. The aim of the talk is to present several methods based on Qingshuo Song Linear Matrix Inequalities (LMI) to analyze properties and City University of Hong Kong to design control laws for systems modeled by fractional Department of Mathematics differential equations. First, model is written as a pseudo [email protected] state space representation whose limitations are reminded. Then, LMI formulations for stability analysis, stabilization and H∞ control are proposed. Finally, some perspectives MS22 are drawn in order to overcome the limitations induced by A Multi-Scale Approach to Limit Cycles with Ran- pseudo state space representation. dom Perturbations Involving Fast Switching and Small Diffusion Christophe Farges University of Bordeaux, IMS Laboratory (CRONE Team), This talk is devoted to multi-scale stochastic systems. The CNRS UMR 5218 motivation is to treat limit cycles under random perturba- [email protected] tions involving fast random switching and small diffusion, which are represented by the use of two small parameters. Jocelyn Sabatier Associated with the underlying systems, there are averaged University of Bordeaux, IMS Laboratory (CRONE Team) or limit systems. Suppose that for each pair of the param- CNRS UMR 5218 eters, the solution of the corresponding equation has an [email protected] invariant probability measure με,δ, and that the averaged equation has a limit cycle in which there is an averaged oc- 0 cupation measure μ for the averaged equation. Our main MS23 ε,δ 0 → effort is to prove that μ converges weakly to μ as ε 0 Diffusive Representations for the Stability Analysis → and δ 0 under suitable conditions. We also examine ap- and Numerical Simulation of Fractional PDEs plication to a stochastic predator-prey model. Moreover, some numerical examples will also be reported. Fractional integrals and derivatives can be equivalently transformed into Diffusive representations, allowing for H.N. Dang well-posedness and stability analysis of fractional ODEs Wayne State University or PDEs, seen as coupled systems. Though a Lyapunov [email protected] functional can be proposed explicitely, a lack of pre- compactness of the trajectories is to be found, we resort N.H. Du to Arendt-Batty theorem to conclude on asymptotic sta- Hanoi National University bility. Moreover, on a linear fractional wave equation with [email protected] non-constant coefficients, a more general Integral repre- CT15 Abstracts 97

sentation is used to analyze and numerically simulate the distributed systems. Computational aspects of optimal ac- system in low dimension. tuator placement are addressed. Main ideas are illustrated with several telling examples. Thomas H´elie CNRS UMR 9912 Miroslav Baric Ircam Centre Georges Pompidou United Technologies Research Center [email protected] East Hartford [email protected] Denis Matignon ISAE-Supaero, University of Toulouse Michael Dellnitz [email protected] University of Paderborn [email protected] Christophe Prieur CNRS Grenoble Stefan Klus [email protected] Freie Universitat Berlin [email protected]

MS23 Stabilizability Properties of Fractional Delay Sys- MS24 tems of Neutral Type Observation and Control of Ensembles of Linear Systems We consider the stabilizability of fractional delay systems of neutral type including the delicate case of systems which Parameter dependent linear systems define natural classes possess a chain of poles clustering the imaginary axis. Frac- of ensembles, i.e., infinite networks of systems. We apply tional rational controllers are investigated first and are methods from complex approximation theory to character- shown to be very efficient for proper systems but not be well ize controllability and observability for ensembles of linear adapted for strictly proper systems with some parameter systems, where the controls or observations are indepen- uncertainties. Second, the stabilizability by some classes dent of the system parameters. By sampling at finitely of fractional controllers with delays is examined. Finally, many parameters, this leads to new tools for robust con- some illustrative examples are given. trol and estimation of large scale networks.

Le Ha Vy Nguyen, Catherine Bonnet Uwe R. Helmke Inria Universitat Wuerzburg [email protected], [email protected] Department of Mathematics [email protected]

MS23 Schoenlein Michael On the Two Degree-of-Freedom Control of Frac- Institute of Mathematics, University of Wuerzburg, tional Systems Germany [email protected] We propose a methodology to design a two-degree-of- freedom fractional control system. First, the feedback controller is obtained, for a class of fractional systems, by solv- MS24 ing a weighted H∞ model-matching problem to achieve Dynamic Intrinsic Variables for Data Fusion and some robustness specifications. Then, an optimal para- State Reconstruction metric feedforward signal is synthesized by input-output inversion of the fractional system dynamics. Finally, the In this talk, we show how data-driven Koopman spec- weighting function and the feedforward signal parameters tral analysis can be applied to the problem of data fusion are optimized through a combined min-max problem. and/or nonlinear state estimation. Our approach uses Ex- tended Dynamic Mode Decomposition to approximate the Fabrizio Padula leading Koopman eigenfunctions, which we use as a set Dipartimento di Ingegneria dell’Informazione of intrinsic coordinates that embed different sets of mea- Università degli Studi di Brescia surements in a common space. We apply our method to [email protected] the FitzHugh-Nagumo PDE, and map point-wise measurements to principal component coefficients. Antonio Visioli University of Brescia I. G. Kevrekidis Department of Mechanical and Industrial Engineering Princeton University [email protected] [email protected]

Matthew O. Williams MS24 Program in Applied and Computational Mathematics Sensing and Control in Symmetric Networks Princeton University [email protected] We examine the relation between the symmetry structure of linear finite-dimensional systems and their controllability, where symmetry property indicates that the state tran- MS24 sition matrix A commutes with a finite non-trivial group A Chaotic Dynamical System That Paints and of matrices. We show that representation theory of finite Samples groups constitutes a framework that allows generalization of some existing results on controllability of interconnected In this work, we develop a novel algorithm to reproduce 98 CT15 Abstracts

paintings and photographs. Combining ideas from ergodic Stamatios Katsikas theory and control theory, we construct a chaotic dynam- University of Warwick ical system with predetermined statistical properties. Be- [email protected] yond reproducing paintings this approach is expected to have a wide variety of applications such as uncertainty quantiﬁcation and sampling for eﬃcient inference in ma- MS25 chine learning. We then explore the use of this algorithm for assigning limited resources to nodes in a graph. Study of Certain Stochastic Predator-Prey Models

Tuhin Sahai Stochastic Predator-Prey models arise from many appli- United Technologies cations in ecological and biological applications. Recently [email protected] such systems have drawn resurgent attentions. In this talk, we present some new perspective of study on such sys- George A. Mathew tems. We treat permanence and ergodicity for both non- University of California, Santa Barbara degenerate and degenerate cases. One new feature of our [email protected] result is the characterization of the support of a unique invariant probability measure. Convergence in total vari- Amit Surana ation norm of transition probability to the invariant mea- System Dynamics and Optimization sure is also established. Related Kolmogorov systems with United Tecnologies Research Center (UTRC) regime switching will also be investigated. [email protected] H.N. Dang Wayne State University MS25 [email protected] Bang-Bang Type Nash Equilibrium Points for Nonzero-Sum Stochastic Differential Games N.H. Du Hanoi National University It is by now well known that non-zerosum differential [email protected] games are connected to multi-dimensional BSDEs with, usually, non Lipschitz generators. In the case when the George Yin payoffs of the players of the game depend only on the ter- Wayne State University minal value of the controlled system, the generator of the Department of Mathematics associated BSDE could even be discontinuous. However [email protected] we show that a Nash equilibrium point for this specific game exists in the Markovian framework. This Nash equilibrium point is of bang-bang type. This is a joint work by MS26 S.Hamadne and Rui MU. Numerical Approaches for Bilevel Optimal Control Said Hamadene,RuiMu Problems with Scheduling Tasks University of Le Mans [email protected], [email protected] Abstract not available.

MS25 Matthias Gerdts Universitaet der Bundeswehr Muenchen Credit Default Swaps with Bessel Bridges [email protected] In this work we propose the valuation of credit default swap using the so-called Bessel bridges to model the credit ndex process. The intuition behind this assumption is that MS26 Bessel bridges, by contruction, remain stricly positive until An Example of Solving Hjb Equations Using Sparse a fixed time T at which they hit zero for the first time. Grids Gerardo Hernandez-del-Valle Banco de Mexico In this presentation, we show an example of solving the 6-D [email protected] HJB equation for the optimal attitude control of a satellite equipped with momentum wheels. To mitigate the curse- of-dimensionality, a computational method on sparse grids MS25 is developed. The method is causality free, which enjoys the advantage of perfect parallelism. The problem is solved Evolutionary Inspection Games using several hundred CPUs in parallel. The accuracy of In this talk, we present a few developments of inspection the numerical solution is verified at a set of randomly se- games with an evolutionary perspective and the properties lected sample points. of their equilibria. Wei Kang Wei Yang Naval Postgraduate School University of Strathclyde Department of Applied Mathematics [email protected] [email protected]

Vassili Kolokoltsov Lucas Wilcox Statistics Dept, University of Warwick Department of Applied Mathematics [email protected] Naval Postgraduate School CT15 Abstracts 99

[email protected] have been expressed. There are several ways to introduce this type of equation. It involves an argument that is a probability measure, and Lions has proposed to work MS26 with the Hilbert space of square integrable random vari- Optimal Control of a Hyperbolic Conservation Law ables. So writing this equation is an issue. Its origin is Modeling Highly Re-Entrant Manufacturing Sys- another issue. In this talk we discuss these various as- tems pects, and for the modeling we heavily rely on a seminar by P.L.Lions at the College de France on November 14, Highly re-entrant manufacturing systems common in semi- 2014; see http://www.college-de-france.fr conductor manufacturing may be modeled by hyperbolic conservation laws with non-local velocity. We investi- Alain Bensoussan gate the problem for L1 and positive measure-valued data, The University of Texas at Dallas and whereas previous results [Coron, Kawski, and Wang (2010) City University of Hong Kong, Hong Kong MR 2679644] and [Colombo, Herty, and Mercier (2011) MR [email protected] 2801323] established existence and uniqueness of solutions for the minimum-time optimal control problem and for L2 data. MS27 On Nonlinear Filtering Theory for McKean-Vlasov Matthias Kawski SDEs Dept. of Mathematics and Statistics Arizona State University Partially observed stochastic dynamical systems whose [email protected] state equations are of McKean-Vlasov (MV) SDE type (and hence contain a measure term) are considered. Non- linear filtering equations are provided based on the classifi- MS26 cation that the measure term is stochastic or deterministic, TheRoleoftheObjectiveinOptimalControl and that either the state or the joint state and measure Problems Arising in Biomedical Applications term is estimated. The filtering equations in both normal- ized and unnormalized forms and, for some cases, equations Mathematical models for biomedical problems generally for conditional densities are obtained. are described by nonlinear systems, often affine in the controls that represent, for example, drug concentrations in Nevroz Sen models for cancer chemotherapy or vaccination and treat- Dept of Electrical and Computer Eng ment rates in epidemiological problems. It is natural to McGill University consider these problems as optimization problems, for ex- [email protected] ample, to minimize the tumor volume achievable with a given amount of chemotherapeutic agents. As much as biology offers insights into the dynamics of the underlying Peter E. Caines system, there generally is little guidance about the choice McGill University of the objective and this allows for considerable freedom. [email protected] However, this choice strongly influences the structure of optimal solutions seen. For example, controls are continuous MS27 if quadratic, L2-type functionals are minimized, but generally have discontinuities if L1-type functionals are con- From Kinetic to Macroscopic Models Through Lo- sidered. Necessary conditions for optimality based on the cal Nash Equlibria Pontryagin maximum principle allow the computations of extremals, but even in the L2 case do not guarantee even We propose a mean field kinetic model for systems of ra- local optimality of a numerically computed solution. Thus tional agents interacting in a game theoretical framework. sufficient conditions for optimality need to be verified and This model is inspired from non-cooperative anonymous these need to be customized to the problem under consid- games with a continuum of players and Mean-Field Games. eration. In this talk, we discuss the implications that the The large time behavior of the system is given by a macro- choice of the objective has on the mathematical procedures scopic closure with a Nash equilibrium serving as the local that need to be employed (e.g., differences in the associ- thermodynamic equilibrium. Applications of the presented ated flows of extremals) as well as relate the structure of theory to social and economical models will be given. solutions back to the biological background of the original problem. Pierre Degond Imperial College of London, Applied mathematics Dpt Heinz Schaettler [email protected] Washington University [email protected] MS27 Urszula Ledzewicz Nonlinear Filtering Problems in Partially Observed Southern Illinois University, USA MFG Control Theory [email protected] In Mean Field Games (MFG) with a major and many mi- nor agents the best response policies of the minor agents MS27 depend on the major agents state and the stochastic mean On the Interpretation of the Master Equation field. The situation where the minor agents partially observe the major agent’s state is considered and nonlinear Since its introduction by P.L.Lions in his lectures and filtering equations for the major agent’s state when its dy- seminars at the College de France, the Master equation namics depend upon the mean field are obtained. The re- has attracted a lot of interest, and various points of view sults are then applied to the corresponding MFG problem. 100 CT15 Abstracts

composition (POD) is applied. By utilizing POD in a trust region framework we can guarantee that the reduced-order Nevroz Sen approximation of the gradient is suﬃciently accurate. Nu- Dept of Electrical and Computer Eng merical results are presented and discussed. McGill University [email protected] Sabrina Rogg University of Konstanz Peter E. Caines Department of Mathematics and Statistics McGill University [email protected] [email protected] Stefan Trenz Universit¨at Konstanz MS28 Department of Mathematics and Statistics On Pod and Krylov Methods for Solution of Alge- [email protected] braic Riccati Equations

We propose a projection based method to solve large-scale MS28 algebraic Riccati equations based on proper orthogonal de- Rb-Based Optimization with Parameter Functions composition. The method can take advantage of existing simulation codes for linear systems, is easy to implement We solve parabolic partial differential equations using a and produces very accurate solutions. We highlight con- space-time variational formulation. We do not only allow nections to Krylov subspace methods and present a numer- parameters in the coefficients (for e.g. model calibration) ical example, where the matrices come from a high fidelity but choose the initial condition as a parameter (function) discretization of a two dimensional PDE. as well. A reduced basis method is introduced that handles the parameter function and the corresponding infinite Boris Kramer dimensional parameter space in a two-step Greedy proce- Virginia Tech dure. In option pricing, this offers the possibility to use [email protected] the same reduced basis for different types of options as they differ only by their initial value (assuming the same John Singler model approach). This is joint work with Antonia Mayer- Missouri S&T hofer (Univ. of Ulm). Mathematics and Statistics [email protected] Antonia Mayerhofer University of Ulm [email protected] MS28 On Adi Approximate Balanced Truncation Karsten Urban Institute of Numerical Mathematics, University of Ulm Balanced truncation is a model reduction method for [email protected] input-output-systems governed by ordinary differential equations which relies on the determination of the observability and controllability Gramian matrices and provides MS29 an error bound in the H∞ norm. A variety of efficient nu- Acyclic Gambling Games merical methods have been developed for balanced truncation. In particular, the ADI iteration for determining the A gambling game is a two player zero stochastic game, Gramians has become very popular since it allows to de- played in discrete time, where each player controls a gam- termine reduced order models of large-scale systems. Since bling house. A gambling house Γi of player i is a measur- ADI iteration provides approximative solutions, it is natu- able function that assigns to each xi ∈ Xi a nonempty set ral to wonder the effect of this approximation in the overall Γi(xi) of probability measures defined on the Borel sub- model reduction process. This is subject the talk, where i i sets of X ,whereX is a metric compact set. Think to we aim to present a backward error analysis: We first show two players in a Casino where xi is the fortune of player that ADI approximate balanced truncation in theory con- i i i and Γ (x ) is the set of gambles available to player i sists of exact balanced truncation of a certain artificial sys- when his fortune is xi. The gambling game is played as tem, which is obtained from the original system via an L2- follows. At stage t =1, ..., knowing the past history of orthogonal projection of the impulse response. Numerical 1 2 1 2 states (x1,x1, ..., xt ,xt ), each player i chooses simultane- consequences will be presented. i i i ously as his opponent a probability σt ∈ Γ (xt). The new i i Timo Reis states xt+1, i =1, 2, are selected according to σt. The pair 1 2 Technische Universität Hamburg-Harburg (xt+1,xt+1) is publicly announced and the game moves to [email protected] stage t+1. For each discount factor λ ∈]0, 1[, one can asso- ∞ t−1 1 2 ciate a game with total payoff t=1 λ(1 − λ) u(xt ,xt ), where u is some continuous utility function. A standard MS28 approach proves that this discounted game has a value vλ, Trust Region POD for Optimal Control of a Semi- which is the unique fixed point of a λ-Shapley operator. linear Heat Equation We prove that, if the gambling houses are non-expensive and irreversible, the asymptotic value limλ→0 vλ exists and An optimal control problem governed by a semilinear heat may be characterized as the unique fixed point of a pair of equation is solved using globalized inexact Newton meth- functional equations which extends the Mertens-Zamir sys- ods. The Newton step is computed by a conjugate gradi- tem and the “Réduite’ operator. ent algorithm. To reduce the computational effort a model order reduction approach based on proper orthogonal de- Rida Laraki CT15 Abstracts 101

CNRS and LAMSADE, Paris-Dauphine University strategy which is -optimal in any n-stage POMDP, pro- [email protected] vided that n is big enough. Moreover, under this strategy, the expectation of the liminf of the random mean of the Jérôme Renault stage rewards is close to the optimal reward. Gremaq, UniversitédeToulouse [email protected] Bruno Ziliotto TSE Univ Toulouse 1 [email protected] MS29 Denjoy-Wolff Theorems for Hilbert’s and Thomp- Xavier Venel son’s Metric Spaces Paris 1 University [email protected] We shall discuss some recent results concerning the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with MS30 respect to Hilbert’s metric or Thompson’s metric. Among Conjugate Times and Regularity of the Minimum other results, we show several Denjoy-Wolff type theorems Time Function with Differential Inclusions that confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We shall also We study the regularity of the minimum time function, T , see how one can extend, and put into a broader perspec- for a system with a general target, taking the state equation tive, results by Gaubert and Vigeral concerning the linear in the form of a differential inclusion. We first derive a escape rate of such nonexpansive mappings. sensitivity relation which guarantees the propagation of the proximal subdifferential of T along any optimal trajectory. 2 Bas Lemmens Then, we obtain the local C regularity of the minimum SMSAS, University of Kent time function along optimal trajectories by using such a [email protected] relation to exclude the presence of conjugate times. Piermarco Cannarsa Brian Lins University of Rome ”Tor Vergata”, Italy Hampden-Sydney College [email protected] [email protected]

Roger Nussbaum MS30 Mathematics Department Second Order Sensitivity Relations for the Mayer Rutgers University Problem in Optimal Control [email protected] We investigate the value function, V, of a Mayer optimal Marten Wortel control problem. The second order sensituivity relations North-west University, Potchefstroom, South Africa are derived using solutions of the corresponding Riccati [email protected] equation, the co-state of the maximum principle and second order sub/superjets of V along optimal trajectories. By applying sensitivity analysis to exclude the presence MS29 of conjugate points, we deduce that the value function is The Operator Approach to Zero Sum Games; Ap- twice diﬀerentiable along any optimal trajectory starting plications to Games with short stage Duration at a point at which V is proximally subdiﬀerentiable.

The operator approach to zero-sum repeated games con- Piermarco Cannarsa sists in the study of the properties of the Shapley operators University of Rome ”Tor Vergata”, Italy describing the recursive structure of the game, in order to [email protected] infer asymptotic properties on its values. After recalling important results in the field, we will consider in partic- Helene Frankowska ular the games with short stage duration defined by Ney- CNRS and IMJ-PRG UPMC Paris 6 man (Dynamic Games and Applications, 2013) and estab- [email protected] lish some of their asymptotic properties using the theory of nonexpansive operators in Banach spaces. Teresa Scarinci UPMC (Paris) and U. Roma Tor Vergata Sylvain Sorin [email protected] University Paris 6 [email protected] MS30 Guillaume Vigeral Linear-Quadratic Optimal Control Probems with Université Paris-Dauphine, CEREMADE Infinite Horizon - Maximum Principle, Duality and [email protected] Sensitivity

We consider a class of inﬁnite horizon optimal control prob- MS29 lems in Lagrange form involving the Lebesgue integral with Existence of Pure Optimal Uniform Strategies in a weight function in the objective. This special class of Partially Observable Markov Decision Processe problems arises in the theory of economic growth, in processes where the time T is an exponentially distributed We consider Partially Observable Markov Decision Pro- random variable and in problem of asymptotic feedback cesses. We prove that for any >0, there exists a pure stabilization of a linear control system. The problem is for- 102 CT15 Abstracts

mulated as optimization problem in Hilbert Spaces. These [email protected] considerations give us the possibility to extend the admissible set and simultaneously to be sure that the adjoint variable belongs to a Hilbert space. For the class of prob- MS31 lems proposed, we can proof an existence result as well as Energy Use Forecast and Model Predictive Control Pontryagin type Maximum Principle including transver- of Building Complexes sality conditions. The convex duality theory developed for this problem class provides sensitivity results. In this talk, we present a framework for forecasting and optimization of energy dynamics of building complexes. This Sabine Pickenhain framework integrates a physics-based model with a time- Brandenburg University of Technology Cottbus, Germany series model to forecast and optimally manage building en- [email protected] ergy. Physical characterization of the building is partially captured by a collection of energy balance equations estimated by a least squares technique and data generated MS30 from the EnergyPlus model. The model is then used in an Necessary Conditions for Optimal Control Prob- MPC framework to control set points. lems with Time Delays Mohsen Jafari We report on necessary conditions for free-time opti- Industrial and Systems Engineering mal control problems with time delay, recently derived Rutgers, The State University of New Jersey by Boccia and Vinter. The conditions cover problems [email protected] with general, non-smooth data and incorporate a new transversality-type condition associated with the free end- Seyed Vaghefi time. They are accompanied by sensitivity relations, which Rutgers University describe the effect of small parameter changes on the opti- Industrial and Systems Engineering mal cost. It is shown how the free-time conditions can be a.vaghefi@gmail.com used to compute optimal controls.

Richard B. Vinter MS31 Imperial College, Exhibition Road, London SW7 2AZ, UK [email protected] A Binary Bilevel Algorithm: Application for Real Time Control of a Medium Voltage Electrical Net- work MS31 Reporting from the SO-grid project: we present a new al- Demand Response-Enabled Optimal Control of gorithm to solve binary bilevel programs. At each step HVAC Systems in Buildings of the algorithm, we solve a binary linear slave program, Optimized control of HVAC system can potentially reduce check the feasibility for the master problem, and add a cut signiﬁcant amount of energy consumption of buildings. In if the solution is not feasible. As an application, we show this work, we describe a model predicted control (MPC) how this algorithm can be used to solve a binary bilevel framework that optimally computes the control proﬁles of model for real time control of medium voltage electrical the HVAC system considering the dynamic demand re- network. sponse signal, on-site storage of electricity, on-site gener- Pierre-Louis Poirion ation of electricity, greenhouse gas emission as well as oc- LIX-Ecole Polytechnique cupants comfort. The approach would determine how to [email protected] power the HVAC system from the optimal combination of grid electricity, on-site stored electricity and on-site generated electricity. Sonia Toubaline, Leo Liberti Ecole Polytechnique Raya Horesh [email protected], IBM T.J. Watson Research Center [email protected] [email protected] Claudia D’Ambrosio Young M. Lee CNRS,LIX,France IBM T.J. Watson Reseach Center [email protected] [email protected] MS31 Leo Liberti IBM ”T.J. Watson” Research Center, Yorktown Heights, Real Time Control of Medium Voltage Electrical USA Distribution Networks LIX, Ecole Polytechnique, Palaiseau, France [email protected] Several electrical measurement devices are designed, developed and deployed within the SO-grid project in order to monitor and control a medium voltage electrical network in Young Tae Chae real time. We present a mathematical model to determine Hyundai Engineering & Construction Co., Ltd the minimum number and location of these devices to be Research and Development Division , Seoul, Republic of placed in the network and that ensure the convergence of Korea the state estimation function. We also discuss some solu- [email protected] tion methods and preliminary computational results.

Rui Zhang Sonia Toubaline IBM T.J. Watson Reseach Center Ecole Polytechnique CT15 Abstracts 103

[email protected] Yuting Mou Zhejiang University Pierre-Louis Poirion [email protected] Ecole polytechnique [email protected] Minyue Fu University of Newcastle Leo Liberti [email protected] Ecole Polytechnique [email protected] Zhiyun Lin Zhejiang University Claudia D’Ambrosio [email protected] CNRS,LIX,France [email protected] MS32 Incorporating Smart-Grid Operating Strategies MS32 into Off-Grid Electrification Planning Optimal Distributed Control for Continuum Power Systems The introduction of smart meters with wireless communication and sophisticated technology for fine-grained mon- Large electrical power networks can be viewed as contin- itoring and control has revolutionized the possibilities for uum systems which follow the dynamics of a second or- deploying highly resilient and economically sustainable mi- der nonlinear wave equation with constant voltage assump- crogrids for off-grid electrification. Traditional planning tions. In this talk we generalize to time and space variant tools lack the flexibility to explore implications of operating voltages. Two optimal control problems are solved. The strategies that leverage these capabilities. A new method is first problem is when the mechanical power is the control presented for incorporating low-level, user-selected power input, while the second problem is when the variant voltage management policies into comprehensive microgrid plan- magnitude is the control input under a generalized variant ning analysis to support comparative evaluation of alter- voltage PDE constraint. Numerical results are presented native implementations for first-access energy systems. to illustrate the performance of the resulting closed loop control systems for large power networks. Jesse Thornberg, Gabriela Hug Carnegie Mellon University Samir Sahyoun [email protected], [email protected] University of Tennessee [email protected] Taha Salim Ustin Carnegie Mellon University in Rwanda Seddik Djouadi [email protected] Department of Electrical Engineering and Computer Science University of Tenneessee, Knoxville Anthony Rowe, Bruce Krogh [email protected] Carnegie Mellon University [email protected], [email protected] K. Tomsovic University of Tennessee MS32 [email protected] Randomized Policies for Demand Dispatch Suzanne M. Lenhart University of Tennessee The paper concerns automated demand response from Department of Mathematics on/off loads. It is assumed that there is one-way communi- [email protected] cation from the grid operator to each load. The loads are either on or off – their power consumption is not continuously variable. Local control at each load is defined by a family of MS32 Markov transition matrices, denoted {Pζ : ζ ∈ }.Attime t, if the load receives the signal ζt from the grid operator, Decentralized Charging and Discharging Control of then it changes state to the value x with probability de- Plug-in Electric Vehicles for Peak Load Shifting fined by the transition matrix, Pζt (x, x ); the randomness Plug-in electric vehicles (PEVs) are energy storage devices is local, and hence independent of all other loads. A mean- and distributed energy resources. Using advanced meter- field limit is used to obtain an input-output model, where ing infrastructure and communication technologies, we can the output is the aggregate power consumption. The main control PEVs for peak load shifting. In this paper, by result is to show how these transition laws can be designed allowing bidirectional power flow between PEVs and the so that the linearized mean field model is minimum phase grid, we study the load flattening problem by regulating at any operating point. This is achieved through a vari- PEVs’ charging and discharging process. A decentralized ety of Markov chain analytical tricks based on Poisson’s algorithm using iterative water-filling is developed. The equation. advantages of our algorithm include reduction in computational burden and privacy preserving. Ana Busic INRIA Hao Xing [email protected] Zhejiang University Hangzhao, China Sean Meyn,YueChen [email protected] University of Florida 104 CT15 Abstracts

[email protected], yuechen@uﬂ.edu [email protected]

Weldon Lodwick MS33 Department of Mathematical Sciences Moreau Sweeping Processes on Banach Spaces University of Colorado Denver [email protected] The sweeping process or Moreau’s process in a Hilbert space (introduced and studied by J.J. Moreau in J.D.E. in 1977) is an interesting problem in both Analysis and Me- MS33 chanics. In this talk I will present my last recent results on the existence of solutions for several extensions to Banach Differential Inclusions and Applications spaces of Moreau sweeping processes and its variants. My talk will deal with differential inclusions. Such evolu- Messaoud Bounkhel tion problems appear when the state-variable is submitted Department of Mathematics to some constraints and therefore has to stay in an admis- King Saud University, Saudi Arabia sible set. Especially we will be interested in the study of [email protected] sweeping processes and of second order differential inclusions involving proximal normal cones. We propose to de- tail some results about these different problems by pointing MS33 out the geometrical assumptions regarding the admissible Control of Moreau’s Sweeping Process: Some Re- sets. Furthermore we will consider some applications in sults and Open Problems crowd motion modelling and in granular media.

In this talk we discuss some recent results of the theory Juliette Venel of Moreau’s sweeping processes including necessary condi- Lab de Mathematiques et leurs Applications de tions for the dynamic case. As open problems we discuss Valenciennes the dynamic programming for the controlled sweeping pro- Universite Lille-Nord de France cess, which is currently being investigated and establishing [email protected] a suitable version of Pontryagin Maximum principle.

Giovanni Colombo MS34 University Padova Dipartimento di Matematica A Dynamic Domain Decomposition for a Class of [email protected] Second Order Hamilton-Jacobi Equations

We present a new parallel algorithm for the numerical so- MS33 lution of a class of second order Hamilton-Jacobi equations Differential and Difference Inclusions and the Fil- coming from stochastic optimal control problems. The ippov Theorem new method is an extension of the patchy domain decomposition technique developed in the recent joint work of This is a joint work with R. Baier and F. Lempio. We the author with E. Cristiani, M. Falcone, and A. Picarelli survey some results on the continuous and discrete Filip- (2012). The original method is modified to solve quite gen- pov theorem on approximate solutions of differential and eral nonlinear problems with possibly degenerate and con- difference inclusions and applications. trol driven diffusion. In particular, we show that, under suitable relations between the data and the discretization Elza M. Farkhi parameters, a remarkable acceleration of the parallel com- Tel Aviv University putation can be obtained. This is a joint work Maurizio School of Mathematical Sciences Falcone. [email protected] Simone Cacace Dipartimento di Matematica MS33 UniversitàdiRoma Optimality Conditions for Optimal Control Prob- [email protected] lems with Interval-Valued Objective Functions

This work examines continuous time optimal control prob- MS34 lems with interval-valued objective functions. For this, we consider three concepts of order relations in the interval Convergence of An Hp-Collocation Method for Op- space to obtain optimality conditions for these problems timal Control and obtain Pontryagin maximum principle type of optimality conditions for optimal control problems using the A convergence theory is introduced for approximations of concept of generalized Hukuhara derivative (gH-derivative) continuous-time optimal control problems using an hp- for interval-valued functions. We also illustrate our method collocation method based on Radau quadrature. Under as- with numerical examples. sumptions of coercivity and smoothness, an hp discretization of an unconstrained control problem has a local mini- Geraldo N. Silva mizer and corresponding Lagrange multiplier that converge Universidade Estadual Paulista - UNESP in the sup-norm to a local minimizer and costate of the Department of Applied Mathematics continuous-time optimal control problem. The accuracy is [email protected] improved either by increasing the degree of the polynomial within a mesh interval or by reﬁning the mesh. The con- Ulcilea Leal vergence theorem is presented along with a brief overview Universidade Federal do Mato Grosso do Sul of the proof. This is a joint work with Hongyan Hou and CT15 Abstracts 105

Anil V. Rao. exploited to design robust controllers against parametric uncertainties. Our approach relies on two different non- William Hager smooth optimization techniques which operate in controller University of Florida and parameter spaces, respectively. Applications reveal a hager@ufl.edu good balance between flexibility and effectiveness.

Pierre Apkarian MS34 ONERA-CERT Optimal Control for Irrigation Scheduling based on [email protected] the AquaCrop Model

We present a methodology based on numerical optimal con- MS35 trol to determine optimal irrigation scheduling under re- Robust Interference Control for Networks with stricting water quotas. The objective function, which is Link Uncertainty nonlinear and non-smooth, is the expected seasonal yield calculated using the dynamic crop model AquaCrop. By In multi-cell communication networks, the end users suf- gradually increasing the value of the water quota, the con- fer not only from intra-cell interference and noise, but also vex function describing yield as a function of irrigation wa- inter-cell interference. It is very important to control these ter as obtained. Irrigated maize in the region of Lombardia, interferences by precoding the transmitted signals to im- Italy, is presented as example. prove the quality of the received signals and maximize the network throughput. Signal precoding must use the link Raphael Linker state information, which is obtained through training and Technion thus subject of uncertainty. In this talk, we show that the [email protected] robust interference control is a concave program, which can be solved effectively by very low-complexity iterations. MS34 Tuan Hoang Computation of An Explicit Error Estimate for Op- University of Technology, Sidney, Australia timal Control Problems of Odes Faculty of Engineering and Information Technology [email protected] Error estimates for the local solution of an optimization problem typically depend on the fineness of the discretization and on the smallest eigenvalue of a certain quadratic MS35 form (related to second-order sufficient optimality conditions). In this talk, we will consider the case of optimal Bilinear Constrained Programming for Robust PID control problems of ODEs, discretized in time. The com- Controller Design putation of the smallest eigenvalue, a delicate task, will be A new design method of extended PID controllers achiev- based on a ”Riccati”-based approach, that we will explain ing robust performance is developed. Both robust stabiliza- with the help of Schur complements. tion and performance conditions are losslessly expressed by Laurent Pfeiffer bi-linear constraints in the proportional-double derivative University of Graz gains (kp,kdd) and the derivative-integral gains (ki,kd). laurent.pfeiff[email protected] Therefore, the considered PID control design can be efficiently solved by alternating optimization between (kp,kdd) and (ki,kd), where each alternating iteration is an infi- MS34 nite linear or infinite convex program. Furthermore, the Lie Brackets and Hamilton-Jacobi Inequalities method works equally efficiently whenever even higher order differential or derivative terms are needed to be in- In relation with a control-affine system with a non nega- cluded in PID control to improve its robust stabilizability tive Lagrangian, we embed the corresponding Hamilton- and performance capability. Numerical examples are pro- Jacobi-Bellman equation in a more general equation. In vided to show the viability of the proposed development. particular, the latter is built from Lie brackets of the vector fields involved in the dynamics. The supersolutions of this Shigeyuki Hosoe extended equation can be regarded as Liapunov-like func- RIKEN-TRI Collaboration Center for Human-Interactive tions (here called Minimum Restraint Functions), which, Robot R besides yielding global asymptotic controllability, provide Nagoya, Japan an upper estimate on the minimum value. [email protected]

Franco Rampazzo Universita di Padova MS35 Dipartimento di Matematica Computing the Structured Distance to Instability [email protected] Analysis and control of systems with uncertain real parameters has been high on the agenda since the 1980s. In this MS35 talk we investigate the computation of quantities like the Parametric Robust Control Design distance to instability of a nominally stable system with uncertain parameters, or the worst-case H-inﬁnity norm We present a new technique for tuning arbitrary linear of a system over a given range of uncertain parameters. control structures against multiple plant models subject Such criteria allow to assess the robustness of a system, to parametric uncertainties and against a variety of per- but their computation is NP-hard. We therefore develop formance requirements. Our method is an inner relax- heuristic approaches, which are fast and reliable in prac- ation. Worst-case parametric scenarios are computed and tice,andwhichcanaposterioribecertiﬁedwhenusedin 106 CT15 Abstracts

tandem with suitable global methods. Balázs Gerencsér Université catholique de Louvain Dominikus Noll [email protected] Universite Paul Sabatier Institut de Mathematiques [email protected] MS36 A Classification Based Perspective to Optimal Pol- icy Design for a Markov Decision Process MS36 Parameter Estimation in a Stochastic System Classical approximate dynamic programming techniques Model for PageRank generally become impracticable in high-dimensions. Policy search copes with this issue by considering a parameter- The PageRank algorithm is used by Google as a way of ized policy space. Here, we focus on discrete actions and hierarchically indexing web pages in order to ensure that introduce a parameterization inspired by nearest-neighbor it provides relevant and reputable search results. In this classification, each particle representing a state space re- paper, we present a stochastic system reformulation of the gion mapped into a certain action. Locations and actions PageRank problem and establish strong consistency of the are tuned via policy gradient with parameter-based explo- least squares estimator of an unknown parameter in the ration. The task of selecting an appropriately sized set of system. Furthermore, we show that the least squares es- particles is solved through an iterative scheme. timator remains strongly consistent within a distributed randomized framework for PageRank computation. Giorgio Manganini, Matteo Pirotta, Luigi Piroddi, Marcello Restelli Cody E. Clifton, Bozenna J. Pasik-Duncan Politecnico di Milano, Italy University of Kansas [email protected], [email protected], [email protected], [email protected] [email protected], [email protected]

Maria Prandini MS36 Dipartimento di Elettronica e Informazione Classification of Alzheimer’s Disease Using Unsu- Politecnico di Milano pervised Diffusion Component Analysis [email protected] The goal of this study is to classify magnetic resonance (MR) images of brains of patients with Alzheimers Disease MS36 (AD) and those without AD. An algorithm based on diffusion maps constructs coordinates that generate geometric Shadow Price for General Discrete Time Models representations using the MRI. Diffusion maps arise from modeling of data by stochastic differential equations. This In the case of market with proportional transaction costs method also accounts for variability in calibration for dif- (bid and ask price) we are looking for an artificial mar- ferent patients. This is joint work with Thomas Strohmer ket with price without transaction costs such that opti- from UC Davis. mal strategies and value functions on both markets are the same. In the talk we shall consider a number of problems Dominique Duncan arising in discrete time setting which lead first to so called Department of Mathematics, University of California at weak shadow price, the price depending on current finan- Davis cial position, with the use of which we construct shadow [email protected] price. The talk is based on o joint paper with T. Rogala. Lukasz W. Stettner MS36 Institute of Mathematics [email protected] Empirical Characteristic Function Methods in Sys- tem Identification MS37 The objective of this talk is to extend the empirical characteristic function method to identify finite dimensional Partially Observable Markov Decision Processes linear stochastic systems driven by an i.i.d. noise process, with General State, Action and Observation Sets the characteristic function of which is known to belong to a parametric class of characteristic functions given in closed We describe sufficient conditions for the existence of opti- form. The proposed method is essentially as efficient as mal policies, validity of optimality equations, and conver- the maximum likelihood method. Our results will be sup- gence of value iterations for discounted partially observable ported by extensive numerical experiments. Markov decision processes with Borel state, action, and observation sets. These conditions are: (i) the one-step László Gerencsér cost function is bounded below and K-inf-compact, (ii) the MTA SZTAKI, Hungarian Academy of Sciences, transition probability is weakly continuous, and (iii) the Budapest, Hungary observation probability is continuous in total variation. [email protected] Eugene A. Feinberg MátéMánfay Stony Brook University Goldman Sachs Asset Management International, [email protected] London, Great Britain Pavlo Kasyanov, Michael Zgurovsky [email protected] National Technical University of Ukraine CT15 Abstracts 107

[email protected], [email protected] are given by the flows of two competing Hamiltonians, not necessarily equal to lifts of vector fields. We assume that there are only normal switching points (Kupka, 1987). MS37 Conjugacy for the resulting broken extremals may occur at Inverse Problems and Dynamic Potential Games or between switching times; we formulate a sufficient condition for strong optimality in terms of jumps on the Jacobi Dynamic potential games are, roughly speaking, nonco- fields which is related to the no-fold condition of Noble and operative dynamic games whose equilibria can be found Schättler (2002). As an application, we consider L1 mini- by solving certain optimal control problem. One way to mization of the control of affine multi-input systems whose characterize some classes of dynamic potential games is control is restricted to the Euclidean ball. through inverse problems. In this talk we present some results about inverse problems in optimal control and dy- Jean-Baptiste Caillau namic potential games. In particular, we characterize a Math. Institute class of dynamic potential games whose Nash equilibria Bourgogne Univ. & CNRS and Pareto solutions coincide. [email protected]

David Gonzalez-Sanchez Zheng Chen, Yacine Chitour Escuela Superior de Economia, IPN Univ. Paris Sud & CNRS [email protected] [email protected], [email protected]

MS37 MS38 Equilibrium Characteristics of Default in a Cur- On Suﬃcient Conditions for a Class of Constrained rency Area Problems with Indeﬁnite Quadratic Functional

Hernandez-del-Valle and Martinez-Garcia (2015) find that In [M.M.A. Ferreira, A.F. Ribeiro and G.V. Smirnov, Local default is the optimal decision of a sovereign government in Minima of Quadratic Functionals and Control of Hydro- a currency area after prolonged real exchange rate overval- Electric Power Stations, JOTA, july 2014] some new suffi- uation. Our objective is to determine if default is Pareto cient conditions for a local minimum of a possibly indefinite optimal and/or Nash equilibrium. quadratic functional were developed. That work was motivated by the existence of non-isolated local minimizers Adrian Hernandez-del-Valle associated to a certain class of optimal control problems. Escuela Superior de Economia, IPN We will present some further analysis of such sufficient con- [email protected] ditions as well as some other applications.

Martinez-Garcia Claudia I. M. Margarida A. Ferreira SEPI-ESE-Instituto Politecnico Nacional Universidade do Porto [email protected] Fac. Engenharia, Portugal [email protected]

MS37 G. V. Smirnov Approximation of Denumerable State Continuous- Universidade do Minho Time Markov Games: Discounted and Average [email protected] Payoﬀ Criteria

We consider a two-person zero-sum continuous-time MS38 Markov game with denumerable state space, general action On Strong Local Optimality of Concatenations of spaces, and unbounded payoff and transition rates. We Bang and Singular Arcs deal with noncooperative equilibria for the discounted and the average payoff criteria. We are interested in approxi- Abstract not available. mating numerically the value and the optimal strategies of the game. We construct finite state and actions truncated Laura Poggiolini game models, that can be explicitly solved, which converge Dipartimento di Matematica e Informatica in a suitably defined sense to the original game model. We Universita di Firenze, Italy study the convergence rate for the value of the games and laura.poggiolini@unifi.it we illustrate our results with an application to a population system. MS38 Tomas Prieto-Rumeau The Turnpike Property in Optimal Control Statistics Dept, UNED [email protected] The turnpike property emerged in the 50’s, after the works by the Nobel prize Samuelson in econometry. It stands for JoséMar´ıa Lorenzo the general behavior of an optimal trajectory solution of UCM an optimal control problem in large time. This trajectory [email protected] trends to behave as the concatenation of three pieces: the first and the last arc being rapid transition arcs, and the middle one being in large time, almost stationary, close to MS38 the optimal value of an associated static optimal control No-Fold Conditions for Broken Extremals problem. In a recent work with Enrique Zuazua, we have established the turnpike property in a very general frame- We consider an optimal control problem whose extremals work in finite dimensional nonlinear optimal control. We 108 CT15 Abstracts

prove that not only the optimal trajectory is exponentially Mihailo R. Jovanovic close so some (optimal) stationary state, but also the con- Electrical and Computer Engineering trol and the adjoint vector coming from the Pontryagin University of Minnesota maximum principle. Our analysis shows an hyperbolicity [email protected] phenomenon which is intrinsic to the symplectic feature of the extremal equations. We infer a very simple and eﬃ- Tryphon T. Georgiou cient numerical method to compute optimal trajectories in University of Minnesota that framework, with an appropriate variant of the shoot- [email protected] ing method.

Emmanuel Trelat Universit´e Pierre et Marie Curie MS39 Paris, France Boundary Estimation for Inﬁnite Dimensional El- [email protected] liptic Cauchy Problem Using Observers

MS39 We design and prove the convergence of an iterative ob- A Physics Based Approach to Model Discrepancy server for boundary estimation problem for an elliptic equa- and Model Form Uncertainty for Design and Con- tion, namely, Cauchy problem for Laplace equation. The trol of Distributed Parameter Systems Laplace equation is formulated as a first order system in one of the space variables with state operator matrix. The Abstract not available. convergence of proposed iterative observer is established using semigroup theory and the concepts of observability John A. Burns for infinite dimensional systems. Numerical simulations are Virginia Tech provided to signify efficiency of the algorithm. Interdisciplinary Center for Applied Mathematics [email protected] Meriem Laleg, Mohammed Usman Majeed KAUST [email protected], muhammadus- MS39 [email protected] Optimal Boundary Control and Estimation of Parabolic PDEs Using Sum-of-Squares (SOS) Poly- nomials MS40 We use SOS to design stabilizing and optimal controllers for scalar parabolic PDEs with spatially distributed coef- Model Order Reduction Approaches for the Op- ficients. We use point actuation via Dirichlet, Neumann, timal Design of Permanent Magnets in Electro- Robin and mixed boundary conditions and point measure- Magnetic Machines ments of state. Our approach is based on solving LOIs using a convex parameterization of Lyapunov functions via In an electromagnetic machine with permanent magnets positive matrices. Objectives include include both expo- the excitation field is provided by a permanent magnet in- nential stability and minimum L2 gain. Numerical ex- stead of a coil. The center of the generator, the rotor, amples show the accuracy is competitive with alternatives contains the magnet. Our optimization goal consists in such as backstepping. finding the minimum volume of the magnet which gives a desired electromotive force. This results in an optimiza- Aditya Gahlawat tion problem for a parametrized partial differential equa- Illinois Institute of Technology tion (PDE). We propose a goal-oriented model order reduc- Universite de Grenoble tion approach to provide a reduced order surrogate model [email protected] for the parametrized PDE which then is utilized in the numerical optimization. Numerical tests will be provided in Matthew Peet order to show the effectiveness of the proposed method. Arizona State University [email protected] Alessandro Alla Department of Mathematics University of Hamburg, Germany MS39 [email protected] Low-complexity Modeling of Partially Available Second-order Statistics via Matrix Completion Michael Hinze Universität Hamburg We study the problem of completing partially known state Department Mathematik statistics of large-scale linear systems. The dynamical in- [email protected] teraction between state variables is known while the direc- tionality of input excitation is uncertain. In particular, we seek to explain the data with the least number of possible Oliver Lass input disturbance channels. This can be formulated as a Technische Universitaet Darmstadt Fachbereich rank minimization problem, and for its solution, we employ Mathematik a convex relaxation based on the nuclear norm. [email protected]

ArminZare,YongxinChen Stefan Ulbrich University of Minnesota Technische Universitaet Darmstadt [email protected], [email protected] Fachbereich Mathematik CT15 Abstracts 109

[email protected] Alﬁo.Quarteroni@epﬂ.ch

MS40 MS40 Reduced Basis Method for Multiobjective Opti- Application of Error Estimates for Nonlinear POD mization Reduced Order Models

We present a reduced order technique for the numerical We consider the use of reduced order models in the cal- solution of PDE-constrained multiobjective optimization, ibration of certain models in mathematical finance which where several objective functions have to be simultaneously lead to the identification of parameters of a highly non- optimized. The idea is to find a solution which does not linear PDE. While the ROM fits the original system quite penalize the optimization of any objective function and successfully, the nonlinear dependence is very strong and which is a good compromise for all the individual ones. a frequent refitting of the ROM is necessary. We observed In general, does not exist a single optimal solution, but this numerically and try to find a theoretical justification there exists a (possibly infinite) number of Pareto opti- for this behavior. mal solutions. In the multiobjective optimization theory, the Pareto optimality allows to determine efficient optimal Ekkehard W. Sachs points for all the considered objective functions [C. Hiller- University of Trier meier. Nonlinear multiobjective optimization. A gen- [email protected] eralized homotopy approach. Birkhaeuser Verlag, Basel, 2001]. We apply the reduced basis method in this context where the constraints are given by parametric linear MS41 and semilinear PDEs [A.T. Patera and G. Rozza. Re- Ergodicity Condition for Zero-Sum Games duced basis approximation and a posteriori error estimation for parametrized partial differential equations Version For zero-sum repeated stochastic games, basic questions 1.0. Copyright MIT, http://augustine.mit.edu, 2007], in are whether the mean payoff per time unit is independent order to propose a reduced-order techniques to handle the of the initial state, and whether this property is robust to computational complexity and resolution times and to en- perturbations of rewards. In the case of finite action spaces, sure a suitable level of accuracy. we show that the answer to both questions is positive if and only if an ergodicity condition involving fixed points of the Laura Iapichino recession function of the Shapley operator or reachability University of Konstanz in directed hypergraphs is satisfied. Department of Mathematics and Statistics [email protected] Marianne Akian INRIA Saclay–Ile-de-France and CMAP, Ecole Stefan Volkwein, Stefan Trenz Polytechnique Universität Konstanz [email protected] Department of Mathematics and Statistics [email protected], stefan.trenz@uni- Stephane Gaubert konstanz.de INRIA and CMAP, Ecole Polytechnique [email protected]

MS40 Antoine Hochart Reduced Order Models for Nonlinear PDE- INRIA and CMAP, Ecole polytechnique Constrained Optimization and Control Problems [email protected]

We review reduced basis methods for the efficient solution of parametric optimization and parametrized control prob- MS41 lems dealing with nonlinear PDEs, by considering both a Strategically Enhanced Preferential Attachement, “reduce-then-optimize’ and an “optimize-then-reduce’ ap- Coalition Building and Evolutionary Growth proach. A simultaneous reduction of state and control spaces is performed when dealing with parametrized con- We prove rigorous results on the convergence of various trol problems. Moreover, efficient a posteriori error bounds Markov decision models of interacting small agents to a enable to certify the solution of the reduced optimization deterministic evolution on the distributions of the state problem. We present some numerical test cases dealing spaces of small players, paying the main attention to situ- with the optimal control of fluid flows. ations with an infinite state space of small players. These include the strategically enhanced extensions of the models Andrea Manzoni of evolutionary growth, coalition building and preferential EPFL, MATHICSE-CMCS attachment. Applications include processes of banks or Switzerland firms merging, as well as the processes of emerging coop- andrea.manzoni@epfl.ch eration.

Federico Negri Vassili Kolokoltsov MATHICSE-CMCS, Ecole Polytechnique Fédérale de Statistics Dept, University of Warwick Lausanne [email protected] federico.negri@epfl.ch

Alﬁo Quarteroni MS41 Ecole Pol. Fed. de Lausanne Target Defense Diﬀerential Game with a Closed- 110 CT15 Abstracts

Form Solution Programming on Hybrid Systems

A pursuit-evasion game in the plane is considered where an The notion of hybrid system has been recently introduced attacker (A) strives to come as close as possible to a Tar- to give a unified framework for control systems mixing dis- get set (T) before being intercepted by the Defender (D) crete and continuous control actions. In this talk, we re- whereas D tries to intercept A as far away from T as pos- view some recent researches on the approximation of Dy- sible; the players A and D have simple motion a la Isaacs. namic Programming equations for hybrid systems, includ- The game terminates when A reaches T without having ing convergence and error estimates for numerical schemes, been intercepted by D, or A comes as close as possible to acceleration techniques based on policy iteration, and con- the target set T, at which time he is captured by D. We struction of a quasi-optimal feedback. Moreover, we show also comment on the case where the target T is a dynamic some numerical tests on real (although relatively simple) point target and the D and T team play cooperatively to applications. defeat A. Roberto Ferretti Meir Pachter Dipartimento di Matematica e Fisica Air Force Inst of Technology UniversitàdiRomaTre Dept of Electrical Engineering [email protected] Meir.Pachter@afit.edu Achille Sassi ENSTA ParisTech MS41 [email protected] Development of An Idempotent Algorithm for a Network-Delay Game Hasnaa Zidani ENSTA ParisTech, INRIA Saclay A game is considered where the communication network [email protected] of the first player is explicitly modeled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modeled through MS42 expectations over idempotent probability measures. Idem- Local Optimization Algorithms for the Approxima- potent algebras are used to obtain an algorithm for solution tion of Hamilton-Jacobi-Bellman Equations of the game. We introduce local optimization strategies for Dynamic Amit Pandey Programming-based approximations of Hamilton-Jacobi Univ. California, San Diego equations. In particular, semi-Lagrangian schemes require [email protected] the local minimization of the Hamiltonian with respect to the control variable. For this purpose, we set a semi- William McEneaney smooth Newton method and a first-order primal-dual al- University of California at San Diego gorithm, both leading to accurate optimal control fields. [email protected] We present different examples assessing the performance and accuracy of the proposed scheme.

MS42 Dante Kalise Coupling MPC and DP Methods for the Numerical Radon Institute for Computational Solution of Optimal Control Problems andAppliedMathematics(RICAM) [email protected] We consider the approximation of an infinite horizon optimal control problem which combines a first step based on Axel Kroener Model Predictive Control (MPC) in order to have a quick INRIA Saclay and CMAP, Ecole Polytechnique guess of the optimal trajectory and a second step where we [email protected] solve the Bellman equation in a neighborhood of the reference trajectory. In this way we obtain a local version of Karl Kunisch the classical DP approach. We present the main features Karl-Franzens University Graz of these new technique and illustrate its effectiveness by Institute of Mathematics and Scientific Computing some numerical tests. [email protected] Maurizio Falcone Università di Roma “La Sapienza’, Italy MS42 [email protected] Speeding Up Model Predictive Control Via Al’brekht’s Method and Its Extensions Alessandro Alla Department of Mathematics The methods that we propose for speeding up MPC are University of Hamburg, Germany based on Albrekhts method for solving HJB equations. Al- [email protected] brekht showed that the Taylor series around an operating point of the optimal cost and optimal feedback of an infinite Giulia Fabrini horizon continuous time nonlinear optimal control problem UniversitàdiGenova could found degree by degree. We extend this method to [email protected] discrete time nonlinear optimal control problems. The series provide a terminal cost and terminal feedback for MPC that is defined on a larger domain. This allows a shorter MS42 time horizon thereby speeding up MPC. We extend the se- Recent Computational Techniques for Dynamic ries approach to find the Taylor series of the optimal cost CT15 Abstracts 111

and optimal feedback around a optimal trajectory. This closed control set U ⊂ Rm. Using second order tangents, speeds up MPC by yielding a longer interval for the real we show that if a controlu ¯(·) is optimal, then an associ- time computation. ated quadratic functional is nonnegative on elements in the second order jets to U alongu ¯(·). Our proofs are straight- Arthur J. Krener forward and do not use embedding of the problem into a Naval Postgraduate School class of infinite dimensional problems. Department of Applied Mathematics [email protected] Helene Frankowska CNRS and IMJ-PRG UPMC Paris 6 [email protected] MS43 Second Order Analysis of State-Constrained NikolaiP.Osmolovskii Control-Affine Problems Systems Research Institute, Polish Academy of Sciences ul. Newelska 6, 01-447, Warszawa, Poland In this talk we establish new second order necessary and [email protected] sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state MS43 framework the Goh transform, which is the classical tool A Second-Order Maximum Principle for State- for obtaining a generalization of the Legendre condition. Constrained Control Problems We propose a shooting algorithm to solve numerically this class of problems and we provide a sufficient condition for In this talk we present second-order necessary optimality its local convergence. We present examples to illustrate conditions for control problems in the presence of pure the theory. state constraints, obtained using second-order tangents to the set of trajectories. Through a second-order variational Mar´ıa Soledad Aronna differential inclusion we obtain a point-wise second-order IMPA maximum principle and a second-order necessary optimal- [email protected] ity condition in the form of an integral inequality which extends some earlier known results to the case of strong Frédéric Bonnans local minimizers. Inria-Saclay and CMAP, Ecole Polytechnique [email protected] Daniela Tonon IMJ UPMC Paris 6 Bean-San Goh [email protected] CURTIN SARAWAK RESEARCH INSTITUTE, MALAYSIA Helene Frankowska [email protected] CNRS and IMJ-PRG UPMC Paris 6 [email protected]

MS43 Daniel Hoehener Second-Order Necessary Conditions in Pontryagin MIT Form for Optimal Control Problems [email protected] We say that optimality conditions for an optimal control problem are in Pontryagin form if they only involve La- MS44 grange multipliers for which Pontryagin’s minimum prin- Toward Massive Deployment of Power Electronics ciple holds. This restriction to a subset of multipliers is in Future Electric Energy Systems: Modeling and a strengthening for necessary conditions, and enables suf- Control Challenges and Opportunities ficient conditions to give strong local minima [Milyutin, Osmolovskii]. We consider optimal control problems with In this talk we pose the problem of fast digital control de- pure state and mixed control-state constraints, and we sign for changing electric power systems. The underlying present here first- and second-order necessary conditions modeling, placing and tuning of minimal number of fast in Pontryagin form, relying on a technique of partial relax- nonlinear digital controllers in both microgrids and EHV ation [Dmitruk]. power plants is discussed in light of the state-of-the-art in nonlinear control for general large scale dynamical sys- Frédéric Bonnans, Xavier Dupuis tems. We combine the rich structure of the underlying Inria-Saclay and CMAP, Ecole Polytechnique power system with general methods on the way to a sys- [email protected], [email protected] tematic design framework.

Laurent Pfeiﬀer Marija Ilic University of Graz Carnegie Mellon University laurent.pfeiﬀ[email protected] [email protected]

MS43 MS44 Second-Order Necessary Optimality Conditions for Balanced Control Strategies for Heterogeneous the Mayer Problem Subject to a General Control Battery Systems for Smart Grid Support Constraint This paper introduces new balanced charge/discharge con- We discuss second order necessary optimality conditions trol strategies that distribute charge or discharge currents for the Mayer optimal control problem with an arbitrary properly so that during operations battery pack balancing 112 CT15 Abstracts

is continuously maintained. The strategies are targeted UniversitàdiSiena,ViaRoma56 for serially interconnected heterogeneous battery systems 53100 Siena (Italy) to be used for power grid support. SOC-based balanced [email protected] charge/discharge strategies are developed. Their convergence properties are rigorously established, and simulation Antonio Vicino examples demonstrate their convergence behavior under UniversitàdiSiena different charging current profiles. Also, robustness against [email protected] parameter estimation errors is discussed.

Michael P. Polis Donato Zarrilli Oakland University Universit`adiSiena [email protected] Dip. Ingegneria dell’Informazione e Scienze Matematiche [email protected] Le Yi Wang, Caisheng Wang Wayne State University MS45 [email protected], [email protected] An Optimal Junction Solver for Traﬃc Flow

George Yin Abstract not available. Wayne State University Department of Mathematics Annalisa Cesaroni [email protected] Dipartimento di Matematica Universita di Padova Feng Lin [email protected] Wayne State University fl[email protected] MS45 On the Attainable Set for Scalar Conservation Laws MS44 and Its Application Is Consumer-Based Integration of Renewable and Abstract not available. Storage Good for Consumers? Shyam Sundar Ghoshal Two models of renewable integration and the use of stor- GSSI, Gran Sasso Science Institute age in distribution networks are considered. The first is a L’Aquila, Italy centralized utility-based model in which the utility owns [email protected] the renewable generation as part of its portfolio of energy resources. The second is a decentralized consumer-based model in which each consumer owns the renewable gener- MS45 ation and is allowed to sell surplus electricity back to the On the Uniform Controllability of the One- utility in a net-metering setting. Similar models for storage Dimensional Transport-Diffusion Equation in the are also considered: the utility owned and operated stor- Vanishing Viscosity Limit age vs. consumer owned and operated one. The essential question is whether consumer owned and operated renew- Abstract not available. able generation or storage ultimately benefits the consumer under a profit regulated monopoly. Pierre Lissy Paris-Dauphine University Liyan Jia, Lang Tong Paris, France Cornell University [email protected] [email protected], [email protected]

MS45 MS44 Exact Boundary Controllability of Nodal Proﬁle for Exploiting Energy Storage for Integration of Re- Quasilinear Wave Equations in a Planar Tree-Like newables in Low Voltage Networks Network of Strings

Electricity networks have witnessed the outgrowth of Abstract not available. a huge number of uncertainty sources and constraints, mainly due to the rising amount of renewable generation Ke Wang and the increased sensitivity of customers to quality of Paris-Dauphine University service. We investigate optimal sizing and placement of Paris, France an energy storage to address both over- and under-voltage [email protected] problems in distribution networks. An optimal power ﬂow is formulated where the total storage budget is minimized subject to power ﬂow equations, energy storage dynamics MS46 and voltage quality constraints. A convex relaxation ap- Estimation of a Gaseous Release into the Atmo- proach is exploited to provide a suboptimal solution. sphere Using An Unmanned Aerial Vehicle

Antonio Giannitrapani We propose a scheme based on controls and computational Universita’ di Siena, Italy ﬂuid dynamics to provide real-time estimates of the gas [email protected] concentration released in the atmosphere from a moving source. The concentration is estimated numerically using Simone Paoletti an unmanned aerial vehicle equipped with a gas sensor. CT15 Abstracts 113

The performance-based motion control of the sensing aerial [email protected] vehicle is integrated into the performance state estimation scheme. The resulting guidance scheme couples the vehicle motion to the estimator performance. MS47 Computing Reachable Sets by Distance Functions Nikolaos Gatsonis and Solvers for Optimal Control Problems Worcester Polytechnic Institute [email protected] Reachable sets of nonlinear state-constrained control problems are calculated by solving parametric optimal control Michael A. Demetriou problems with a suitable OCP solver. Here, the feasible set Worcester Polytechnic Institute equals the reachable set and the optimal value coincides [email protected] with the distance function of a grid point to the reachable set. A lower-dimensional projected reachable set of Tatiana Egorova a single-track model for collision avoidance is computed. Worcester Polytechnic Institute Possible speedups of the algorithm by the piecewise lin- [email protected] ear interpolated distance function and parallelization are demonstrated.

MS46 Robert Baier Department of Mathematics, University of Bayreuth LQG Controller Equivalent to the Control by In- [email protected] terconnection for Infinite Dimensional Port Hamil- tonian System MS47 This paper proposes a method that combines LQG control design and structure preserving model reduction for the A Dual Model/Artificial Neural Network Frame- control of infinite dimensional port Hamiltonian systems work for Privacy Analysis in Traffic Monitoring (IDPHS). A modified LQG controller design equivalent to Systems control of IDPHS by interconnection is first proposed. The Most large-scale traffic information systems rely on a com- method of Petrov-Galerkin is then used to approximate the bination of fixed sensors (e.g. loop detectors) and user balanced realization of the IDPHS by a finite dimensional generated data, the latter in the form of probe traces sent port Hamiltonian system and to provide the associated re- by GPS devices on vehicles. While this type of data is rel- duced order LQG controller. atively inexpensive to gather, it can pose multiple privacy risks, even if the location tracks are anonymous. We pro- Yongxin Wu, Boussad Hamroun pose a new framework for analyzing a variety of privacy LAGEP, University Lyon1, 43 Bvd du 11 Nov. 1918 problems arising in transportation systems. 69100 Villeu [email protected], [email protected] Edward Canepa King Abdullah University of Science and Technology Yann Le Gorrec Department of Electrical Engineering FEMTO-ST AS2M, ENSMM [email protected] [email protected] Christian Claudel Bernard Maschke King Abdullah University of Science and Technolgy LAGEP, Université Claude Bernard - Lyon 1 (KAUST) Lyon, France Electrical Engineering and Mechanical Engineering [email protected] [email protected]

MS46 MS47 Robustness of Nonlinear Optimal Regulator for Re- Hamilton-Jacobi Approach for Second Order Traf- duced Distributed Parameter System ﬁc Flow Models

This paper proposes an evaluation index of robustness to While being simple and tractable, the first order LWR disturbances for distributed parameter systems with non- model does not reproduce certain meaningful traffic phe- linear optimal feedback designed by the stable manifold nomenon. Second order traffic flow models have been de- method that is a numerical calculation method of Hamil- veloped to fill this gap. In this talk, I will focus on the ton Jacobi equations, and the POD-Galerkin method that Generic Second Order Model (GSOM) family which em- is a finite dimensional reduction method. We state a robust beds lots of these models. Recasting the GSOM in La- control problem described by POD bases and disturbances. grangian coordinates allows us to use the Hamilton-Jacobi Then, we show that the problem can be formulated as a framework and to deduce a Lax-Hopf type formula which generalized eigenvalue problem. is helpful for numerical resolution.

Gou Nishida Guillaume Costeseque Intelligent and Control Systems Laboratory, Department Inria Sophia Antipolis - M´editerran´ee of Ap [email protected] [email protected]

Noboru Sakamoto MS47 Nanzan University Robust Control Problems - from the Perspective of 114 CT15 Abstracts

Evolution Equations for Sets bridges.

In ”robust” control problem, two types of controls occur Yongxin Chen, Tryphon T. Georgiou and, the user can choose only one of them whereas the other University of Minnesota one is not known exactly (i.e., uncertainty). Whenever all [email protected], [email protected] possibilities for the second control are considered simultaneously, states should be described as sets. We discuss an Michele Pavon extension of differential equations to set-valued states. It University of Padova is illustrated by examples and their numerical solutions. It [email protected] even lays the analytical foundations for control problems with state constraints. MS48 Thomas Lorenz RheinMain University of Applied Sciences On some Connections between Information Theory, Applied Mathematics Nonlinear Estimation and Statistical Mechanics [email protected] In this talk I discuss the connections that exist between Nonlinear Filtering for Diffusion Processes, the Variational MS48 Characterization of Gibbs Measures and Information- theoretic characterization of optimality of nonlinear esti- Linear Stochastic Control with State and Control mators . It relies on T.E. Duncans important work on Dependent Noise the computation of Mutual Information for Diffusion Pro- The control of a linear stochastic system with stochastic cesses. I discuss also the role of Information Theory in the coefficients, linear state and control dependent noise, and context of the Separation Theorem of Stochastic Control, a quadratic cost is formulated and solved. A stochastic Ric- Dual Control and Self Tuning Regulators cati equation is used to obtain the explicit optimal control Sanjoy K. Mitter in a direct way using a decomposition of submartingales LIDS from the running cost and the Lagrangian Grassmannian MIT for the control problem. This problem have been consid- [email protected] ered by some others using different approaches.

Tyrone E. Duncan MS49 University of Kansas Department of Mathematics Homogenization Results for Hamilton-Jacobi [email protected] Equations on Networks

Bozenna Pasik-Duncan Abstract not available. University of Kansas Cyril Imbert [email protected] Paris-Dauphine university [email protected] MS48 Hidden Markov Change Point Estimation MS49 A hidden Markov model is considered where the dynamics Singular Perturbation of Optimal Control Prob- of the hidden process change at a random ‘change point’ T. lems on Periodic Multi-Domains In principle this gives rise to a non-linear filter but closed form recursive estimates are obtained for the conditional In this talk we consider the singular perturbation of an distribution of the hidden process and of T. optimal control problem in which the controlled system involves a fast and a slow variables. The fast variable lives Robert J. Elliott in periodic multi-domains. The problem can be reformu- University of Calgary lated as a Hamilton-Jacobi-Bellman (HJB) equation, while [email protected] the geometric singularity of the multi-domains leads to the discontinuity of the Hamiltonian. Under a controllability Sebastian Elliott assumption on the fast variable, the limit problem has been Elliott Stochastics Inc. analyzed and the associated HJB equation has been ob- [email protected] tained. This equation describes the limit behavior of the value function of the perturbed problem when the scale of periodicity tends to 0. MS48 Zhiping Rao On Cooling of Stochastic Oscillators RICAM, Austrian Academy of Sciences Active control of micro/macro mechanical systems to re- [email protected] duce thermal noise is implemented in atomic force mi- croscopy, polymer dynamics and gravitational wave detec- Nicolas Forcadel tors. For a system of nonlinear stochastic oscillators, we INSA de Rouen consider the problem of feedback controlling the system ef- [email protected] ficiently to a desired steady state corresponding to lower thermal noise both asymptotically and in finite time . The solution (in closed-form in the Gaussian case) involves ex- MS49 tending and adapting the classical theory of Schroedinger The Hamilton Jacobi Equation for Optimal Control CT15 Abstracts 115

Problems with State Constraints turbations destroy exact commutatitivy). This leads directly to questions like when are almost commuting matri- We discuss conditions under which the value function for a ces nearly commuting, i.e., does smallness of commutators state-constrained optimal control problem can be charac- imply proximity to commuting matrices? When the an- terized as the unique generalized solution of the Hamilton swer is yes, existence of Lyapunov functions coupled with Jacobi equation. Special attention is given the interplay a perturbation analysis can be used to show stability and between the validity of this characterization and system to estimate allowable deviations of the commutators from theoretic properties (controllability and monotonicity) of zero. Similar results can be derived for nilpotent or solv- the underlying dynamic constraint and the regularity of able Lie algebras. Among a number of available results the data, and new classes of problems are identiﬁed, for on almost commuting vs. nearly commuting matrices, we which the characterization is possible. work with theLojasiewicz inequality which lower-bounds the value of a polynomial in terms of the distance to its Richard B. Vinter set of zeros. Applied in our framework, theLojasiewicz Imperial College, Exhibition Road, London SW7 2AZ, UK inequality and other related results allow us to obtain ro- [email protected] bust versions of Lie-algebraic stability criteria for switched linear systems. MS49 Daniel Liberzon Optimal Control Problems on Generalized Net- Department of Electrical and Computer Engineering works University of Illinois This talk concerns some optimal control problems on d- [email protected] dimensional networks. We will present a new characterization of the value function as solution to a system Yuliy Baryshnikov of Hamilton- Jacobi- Bellman equations with appropriate University of Illinois at UrbanaChampaign junction conditions. This result doesn’t require the usual Department of Mathematics controllability condition on the junction and it still holds [email protected] when the value function is discontinuous.

Hasnaa Zidani MS50 ENSTA ParisTech, INRIA Saclay Stability of Linear Diﬀerence Equations with [email protected] Switching Parameters and Applications to Trans- port and Wave Propagation on Networks Cristopher Hermosilla ENSTA ParisTech This talk addresses the stability of linear diﬀerence equa- [email protected] tions of the form

N MS50 d x(t)= Ai(t)x(t − Li),x(t) ∈ C , Stabilisation of Dynamical Systems Subject to i=1 Switching and Two Time Scale Phenomena

This talk is dedicated to the problem of stability analysis for positive delays Li. When the matrices Ai are time- and control design of singularly perturbed switched sys- independent, the corresponding autonomous system can tems. The problem of norms computations such as H2 and be analyzed by Laplace transform methods leading to the H infinity norms is presented and the generalization to the well-known Silkowski’s criterion, but this technique fails to case of switching and switched singularly perturbed sys- apply to the non-autonomous case. Using an explicit for- tems is discussed. The talk focuses on open problems for mula for solutions, we get a stability criterion for the non- this class of hybrid systems. We illustrate the different autonomous system. When applied to the case of switching notions and properties discussed in this presentation using matrices Ai(·) subject to arbitrary switching signals, one numerical examples. obtains a criterion in terms of a generalized joint spectral radius, which extends Silkowski’s criterion. Corresponding Jamal Daafouz stability criteria for transport and wave propagation on CRAN, Université de Lorraine networks with variable coefficients are derived by express- [email protected] ing these systems as difference equations. In particular, we show that the wave equation on a network with arbitrarily switching damping at external vertices is exponentially MS50 stable if and only if the network is a tree and the damping Commutators, Robustness, and Stability of is bounded away from zero at all external vertices but one. Switched Linear Systems

The subject of this work is stability analysis of switched Yacine Chitour linear systems, described by a family of continuous-time Univ. Paris Sud & CNRS linear dynamical systems and a rule that orchestrates the [email protected] switching between them. There are well-known results stating that stability is preserved under arbitrary switching provided that certain commutation relations hold between Guilherme Mazanti the matrices being switched, in particular, if the matrices CMAP, Ecole´ Polytechnique commute or generate a nilpotent or solvable Lie algebra. [email protected] The present works aims at obtaining stability conditions along these lines which are robust with respect to suﬃ- Mario Sigalotti ciently small perturbations of the system data (such per- INRIA, Centre de Recherche Nancy - Grand Est 116 CT15 Abstracts

[email protected] an optimization algorithm. The results are supported by examples.

MS50 Andreea Grigoriu Analysis of the Limit Sets of Switched Systems Laboratoire Jacques-Louis Lions Université Paris-Diderot We consider switched systems, both linear and non linear, [email protected] whose trajectories are bounded by a weak Lyapunov function V . We investigate the convergence of the trajectories towards two different locus according to the class of switch- MS51 ing laws considered. For each vector field fi we consider Sparse Time-Frequency Control of Quantum Sys- the set Ki where the derivative of V along fi vanishes, and tems the subset Ni of Ki invariant under fi. The limit sets for inputs with (roughly speaking) dwell-time are contained in We propose an optimal control framework to generate con- the union of the Ni, and the limit sets for general inputs are trol fields with a very simple time-frequency structure. We contained in the union of the Ki. Consequently the asymp- achieve this by using cost functionals in the time-frequency totic properties of such systems are entirely encrypted in plane that enhance sparsity in frequencies and smoothness the geometry of the Ni’s, or the Ki’s, according to the in time. Mathematically this is realized by working in a kind of inputs we consider. In the case of two asymptot- space of function-valued measures. I will give an outline ically stable linear vector fields the asymptotic properties of the proposed control framework, will discuss first order are also related to the observabiliy properties of a related optimality conditions and present numerical results for an system, generally much smaller. To finish we show that a example from molecular control. system which is asymptotically stable for dwell-time inputs but not GUAS possesses trajectories that converge to the Felix Henneke origin as slowly as wanted, but that with a fixed dwell-time Technische Universität München an exponential convergence rate is obtained. These last two Center for Mathematics results can be partially extended to non linear systems. [email protected]

Sa¨ıd Naciri, Philippe Jouan Gero Friesecke LMRS, UniversitédeRouen Centre for Mathematical Sciences [email protected], philippe.jouan@univ- Technische Universität München, Germany rouen.fr [email protected]

Karl Kunisch MS51 Karl-Franzens University Graz Time-Zero Controllability and Density of Orbits for Institute of Mathematics and Scientific Computing Quantum Systems [email protected] For a bilinear finite dimensional closed quantum system 2n−1 on the sphere S we study under which conditions we MS51 can control the system in an arbitrary small time. This Quantum Filtering and Parameter Estimation study is based on representation theory of su(n) and on the equivalence between approximate and exact control- Open quantum systems subject to measurement back- lability for finite dimensional quantum systems, that has action and decoherence are described by stochastic master been recently proved. One interesting fact is that, without equations. We present here a quantum filtering process, additional hypotheses, this result does not extend to the based on the measurement outcomes, to discriminate be- Schroedinger equation as a PDEs. tween different parameter values and we prove its stability. Numerical implementations on simulated and experimen- Ugo Boscain tal data illustrate the interest of this estimation method. CNRS, CMAP Ecole Polytechnique [email protected] Pierre Six Mario Sigalotti Centre Automatiques et Systèmes, Mines-ParisTech INRIA, Centre de Recherche Nancy - Grand Est [email protected] [email protected]

MS52 MS51 Semidefinite Programming for Stochastic Control Theoretical and Numerical Aspects in Control of Open Quantum Systems We formulate constrained stochastic control problem as an infinite dimensional linear program. We use semidefinite We address the problem of controllability of quantum sys- programming (SDP) to approximate the primal and dual tems interacting with an engineered environment,with dy- linear program. As such, we approximate the value func- namics described by a non-Markowian master equation. tion of the optimal control problem from the primal linear The manipulations of the dynamics is realized with both program and we approximate the optimal policy from the a laser field and a tailored non-equilibrium, and generally dual linear program. We discuss computational tractabil- time-dependent, state of the surrounding environment. Lie ity of the SDP algorithm. Furthermore, we illustrate the algebra theory is used to characterize the structures of the approach on a few benchmark case studies. reachable state sets and to prove controllability. In order to ensure certain physical properties of the quantum systems Maryam Kamgarpour optimal control problem are formulated and solved using ETH Zurich CT15 Abstracts 117

Switzerland [email protected] [email protected]

MS53 MS52 Low-Complexity Stochastic Modeling of Turbulent Inference and Stochastic Optimal Control Flows

The path integral control theory describes a class of control Second-order statistics of turbulent flows can be obtained problems whose solution can be computed as an inference either experimentally or via direct numerical simulations. computation. The efficiency of the inference computation Due to experimental or numerical limitations it is often the is related to the proximity of the sampling control to the case that only partial flow statistics are reliably known. optimal control. This forms the basis of a novel adaptive Thus, it is of interest to complete the statistical signature sampling procedure. The adaptive sampling procedure can of the flow field in a way that is consistent with the known be used to compute optimal controls as well as to accelerate dynamics. We formulate a convex optimization problem other Monte Carlo computations. that addresses this challenge.

Bert Kappen Armin Zare SNN Machine Learning Group University of Minnesota Radboud University Nijmegen [email protected] [email protected] Mihailo R. Jovanovic Electrical and Computer Engineering MS52 University of Minnesota Randomized Methods for Stochastic Constrained [email protected] Control

We address ﬁnite-horizon control for a stochastic linear sys- Tryphon T. Georgiou tem subject to constraints on control input and state. A University of Minnesota control design methodology is proposed where the trade- [email protected] oﬀ between control cost minimization and state constraints satisfaction is decided by introducing appropriate chance- MS53 constrained problems depending on some parameter to be tuned.From an algorithm viewpoint, a computationally Crom-Based Closed-Loop Control of a Canonical tractable randomized approach is proposed to provide an Separated Flow approximate solution with probabilistic guarantees about its feasibility for the original chance-constrained problem. Abstract not available.

Maria Prandini Eurika Kaiser Dipartimento di Elettronica e Informazione Institute PPRIME, CNRS Politecnico di Milano [email protected] [email protected] MS53 MS52 Closed-Loop Turbulence Control Using Machine Learning in Mean-Field-Type Teams and Games Learning

We consider mean-field-type stochastic games with con- Abstract not available. tinuous action spaces. We show that one can achieve target actions as risk-sensitive team optima and equi- Bernd R. Noack libria without knowing the underlying payoff functions. Institut PPRIME, CNRS Furthermore, under fairly general settings on Brownian- [email protected] driven state dynamics, one can efficiently approximate risk- sensitive mean-field optima in (expected) Hamiltonian po- MS54 tential games and in games with monotone sub-gradient (expected) payoffs. We then focus on speedup model-free Practical Advances in Data-Driven Koopman Spec- learning techniques. Our result builds upon various un- tral Analysis and the Dynamic Mode Decomposi- certainty quantification and variance reduction techniques. tion The dynamic mode decomposition (DMD) is a technique Hamidou Tembine for approximating the Koopman operator and extracting LSS, CNRS-Supelec-Univ. Paris Sud, France dynamical descriptions of a system from observed snap- [email protected] shot data. Here, we present several variations of DMD that facilitate Koopman spectral analysis in practical contexts involving large, streaming, and/or noisy datasets. We also MS53 show that extending DMD to include additional observ- Symbolic Regression for the Modeling of Control ables can yield more authentic Koopman-based descrip- Functions tions. Each DMD method will be demonstrated on numerical and experimental fluids data. Abstract not available. Maziar S. Hemati Markus W Abel Princeton University Ambrosys GmbH [email protected] 118 CT15 Abstracts

Matthew O. Williams system for output evolution, and thereby develop a frame- Program in Applied and Computational Mathematics work for exploiting linear system estimation, detection and Princeton University control theory for nonlinear systems. We demonstrate our [email protected] framework for modeling and forecasting of time series data, estimating missing sensor data, and anomaly detection. Scott Dawson Princeton University Amit Surana [email protected] System Dynamics and Optimization United Tecnologies Research Center (UTRC) [email protected] Clarence Rowley Princeton University Department of Mechanical and Aerospace Engineering Andrzej Banaszuk [email protected] United Technologies Research Center [email protected]

MS54 MS55 Application of the Koopman Operator to Differen- tial Positivity Pontryagin Maximum Principle for Control Sys- tems on Infinite-Dimensional Manifolds Differential positive systems are systems that infinitesi- mally contract a given cone field. Under mild assump- We present a proof of Pontryagin’s Maximum Principle tions, their solutions asymptotically converge to a one- for control problems on infinite-dimensional Banach man- dimensional attractor, which must be a limit cycle in the ifolds. Our proof makes use of techniques of nonsmooth absence of fixed points in the limit set. We use the spec- analysis, demonstrating their utility even for smooth prob- tral properties of the Koopman operator to show a converse lems. In addition, we introduce the technique of La- theorem for differential positivity: every system is differ- grangian charts for geometric problems of dynamic opti- entially positive in the basin of attraction of a hyperbolic mization and discuss an interesting constraint qualification. limit cycle. Failure of this constraint qualification implies the abnormal case of the Maximum Principle, while its presence allows Alexandre Mauroy removal of endpoint constraints through penalization. University of Liege [email protected] Robert Kipka Queen’s University Fulvio Forni [email protected] University of Cambridge ff[email protected] Yuri Ledyaev Western Michigan University Rodolphe Sepulchre [email protected] University of Cambridge Cambridge, UK MS55 [email protected] A Maximum Principle for Implicit and DAE Sys- tems MS54 The presentation focuses on a nonsmooth maximum prin- Koopman Operator Theory for Dynamical Systems ciple for problems involving implicit control systems. The and Control Practice starting point is a known result in Optimal Control with We discuss current theory and practice of applications of Mixed Constraints by [Clarke et all, in SIAM J. Control Koopman operator methods in dynamical systems and con- Optimization, 2010]. We first extend this result to cover trol and its relationship with computational methods. The some situations where less regularity is assumed. We then approach has recently been extended to associate geomet- illustrate the special features of this result, in the smooth rical objects such as isochrons and isostables - using level and nonsmooth case, with some simple examples. In par- sets of Koopman eigenfunctions. We will also discuss the ticular, we apply it to some special cases, namely control relationship between numerical methods such as Dynamic systems involving semi-explicit differential algebraic equa- Mode Decomposition and Koopman Mode Decomposition, tions. and extensions of theory to stability of nonlinear systems Maria doRosario de Pinho and control. University of Porto Igor Mezic Faculdade de Engenharia University of California, Santa Barbara [email protected] [email protected] Igor Kornienko Universidade do Porto MS54 [email protected] Koopman Spectral Analysis for Estimation, Fore- casting and Detection MS55 The dynamics of observables or system outputs defined Necessary and Sufficient Conditions for Invariance on state space of a (nonlinear) dynamical system evolve of Time Delayed Systems linearly in time in Koopman spectral representation. We exploit this property to construct a linear time invariant In this talk we will present necessary and sufficient condi- CT15 Abstracts 119

tions of invariance for time delayed systems parametrized to Δλ-Laplacians (e.g., Grushin-type operators) as well as by differential inclusions. Weak invariance properties will to Elliptic Operators on Lie groups (e.g., Sub-Laplacians be presented as well as our progress towards character- on Carnot groups). izing strong invariance in this setting. In addition, we will explain the effects of our results towards developing Alessia Kogoj a Hamilton-Jacobi theory for the minimal time problem Università di Bologna, Italy under time delayed constraints. [email protected]

Norma Ortiz-Robinson Virginia Commonwealth University MS56 [email protected] The Minimal Control Time for Degenerate Parabolic Equations of Grushin Type

MS55 We control degenerate parabolic equations of Grushin type: 2 2 An Adaptive Mesh Refinement Algorithm for Op- ∂xx + V (x)∂yy on the rectangle (x, y) ∈ (−1, 1) × (0, 1), timal Control Problems where V ≥ 0 vanishes only on the line x = 0. Our input is a source term supported on parallel strips on each side When solving nonlinear optimal control problems via di- of this line. Previous works with V (x)=|x|2γ proved that rect methods, the time interval is discretized and, most fre- null controllability fails for γ>2, holds arbitrarily fast for quently, equidistant-spacing meshes are used. However, to γ ∈ (0, 1), and requires a positive minimal time for γ =1. achieve the desired accuracy in nonlinear problems, these We prove that this time is the distance of the control strips meshes might have a large number of nodes which, in some from the degeneracy line x = 0 computed using the Agmon cases, prevent the optimizers to find an adequate solution. metric V (x)dx2 instead of dx2. We propose an adaptive time-mesh refinement algorithm, considering different levels of refinement and several mesh Luc Miller refinement criteria. In particular, the local error of the ad- Université Paris Ouest Nanterre La Défense joint multipliers is chosen as a refinement criterion. This [email protected] error can be computed efficiently by comparing the solution to a linear differential equation system – the adjoint equation of the maximum principle – with the numerically MS56 obtained dual variables. Finally, we extend this refinement Intrinsic Random Walks and Diffusion in Sub- algorithm to solve a sequence of optimal control problems Riemannian Geometry in a Model Predictive Control (MPC) scheme. We apply the developed scheme to a problem involving manoeuvres In Riemannian geometry, a possible definition of the of nonholonomic vehicles with state constraints. We show Laplace-Beltrami operator is as the generator of the diffu- that the refinement technique leads to numerical results sion obtained as the limit of geodesic random walks. This with higher accuracy and yet with lower overall compu- coincides with the usual divergence of the gradient. We tational time, when compared with alternative methods. discuss how to extend these definitions in sub-Riemannian geometry, where it is not clear what is an intrinsic random walk and what is an intrinsic volume. Joint work with U. Fernando A. Fontes, Luis Tiago Paiva Boscain and R. Neel. Universidade do Porto [email protected], [email protected] Luca Rizzi CMAP, Ecole Polytechnique, France MS56 [email protected] Null Controllability of Grushin and Kolmogorov Equations MS57 From the controllability viewpoint, degenerate parabolic L2-Induced Gains of Switched Linear Control Sys- partial differential equations have interesting features. De- tems pending on the strength of the degeneracy, null controllability may hold or not; it may also require a geometric In this talk, we present results on L2-gain issues related condition and a positive minimal time. In this talk, proofs to linear control switched systems. For that purpose, we will be explained on prototype equations of Grushin and introduce several concepts of extremal norms in the spirit Kolmogorov type. of the well-known Barabanov norm. Joint work with P. Mason and M. Sigalotti. Karine Beauchard ENS Rennes, France Yacine Chitour [email protected] Univ. Paris Sud & CNRS [email protected]

MS56 A Control Condition for a Weak Harnack Inequal- MS57 ity A Hamilton-Jacobi Approach to Barabanov Norms of Positive Linear Systems We introduce a condition allowing to get a weak Har- nack inequality for nonnegative solutions to linear sec- We study switched positive linear systems, and show that ond order degenerate elliptic equations of X-elliptic type. for these systems, Barabanov norms are equivalent to Roughly speaking, our condition requires that the Eu- weak-KAM solutions of a class of Hamilton-Jacobi PDE. clidean balls of small radius are representable by means of Then, we discuss the application of PDE or semigroup X-controllable almost exponential maps. Our results apply methods to establish the existence of Barabanov norms, 120 CT15 Abstracts

exploiting controllability conditions or contraction prop- namical systems. erties in Hilbert’s projective metric. We investigate the asymptotic behavior of optimal trajectories of the associ- Oliver Mason ated control problem. NUI Maynooth, Ireland [email protected] Vincent Calvez Unite de Mathematiques Pures et Appliquees Fabian Wirth Ecole Normale Superieure de Lyon University of Wuerzburg [email protected] [email protected]

Pierre Gabriel Universit´e de Versailles St-Quentin-en-Yvelines MS58 France An Optimal Device Placement Approach for Semi [email protected] Linear Pde Systems over Irregular Spatial Domains A methodology is presented for placing actuating and sens- Stephane Gaubert ing devices with respect to power criteria for semi-linear INRIA and CMAP, Ecole Polytechnique PDE process systems over irregular spatial domains. The [email protected] PDE is discretized using nonlinear Galerkin’s method with statistically-derived basis functions, Laplace transforms and singular perturbation arguments. A non-convex NLP MS57 is then formulated and solved using an interior point global Resonance of Extremal Norms, Marginal Instabil- search algorithm. The methodology is illustrated on the ity, and Sublinear Growth placement of sensing devices for an environmental process.

We analyse the marginal Instability of switching linear systems, both in continuous and discrete time. That is, we Antonios Armaou are interested in situations where the system is not sta- Department of Chemical Engineering ble, but all trajectories grow less than exponentially. We The Pennsylvania State University disprove two recent conjectures of Chitour, Mason, and [email protected] Sigalotti (2012) stating that for generic systems, the resonance is sufficient for marginal instability and for poly- Michael A. Demetriou nomial growth of the trajectories. We provide an efficient Worcester Polytechnic Institute characterization of marginal instability under some mild [email protected] assumptions on the system. Finally, we analyze possible types of fastest asymptotic growth of trajectories. An example of a marginally unstable pair of matrices with sub- MS58 linear growth is given. This is joint work with V. Protasov. Networked Control of Spatially Distributed Sys- tems Using Quantized and Delayed Sensing and Actuation Raphael Jungers Massachusetts Institute of Technology This work considers the stabilization of spatially- Laboratory for Information and Decision Systems distributed systems with low-order dynamics, using net- [email protected] worked sensors and actuators subject to quantization and communication delays. A finite-dimensional model-based controller that explicitly compensates for communication MS57 disruptions and delays is designed, and its closed-loop stability properties under sensor/actuator quantization are Extremal Norms and Linearization Principles for characterized using Lyapunov techniques. This character- Monotone Systems ization is used to develop sensor/actuator reconfiguration strategies that mitigate the impact of delays and quanti- Extremal norms characterize the exponential growth rate zation on performance. The results are illustrated through for several classes of systems that model time-varying numerical simulations. uncertainty, such as discrete or differential inclusions, or ot use a different terminology switched disrete-time, Nael H. El-Farra continuous-time or differential-algebraic systems. For lin- University of California, Davis ear inclusions that leave a cone invariant it can be shown Department of Chemical Engineering and Materials under a mild irreducibility condition that extremal norms Science exist that respect the order induced by the cone, i.e. the [email protected] extremal norms are monotone. On the one hand this provides a new criterion for the existence of extremal norms, which as corollaries provides new insight in robustness, sta- MS58 bility and sensitivity results that have known proofs relying Sensor Location in Feedback Stabilization of the on the properties of extremal norms. A further application Boussinesq Equations of interest is particular to the case of cone-invariance. Lin- ear inclusions that leave a cone invariant occur naturally as In this talk, we discuss the problem of sensor placement the linearization at fixed point of differentiable monotone in feedback stabilization of a thermal fluid described by inclusions. It turns out that the use of extremal norms the Boussinesq equations. This problem is motivated by in the local stability analysis at fixed points yields sharp the design and operation of low energy consumption build- stability estimates for monotone inclusions, which extend ings. We apply the MinMax compensator design to obtain classical results available for time-invariant monotone dy- a reduced-order observer for state estimation based on the CT15 Abstracts 121

geometric structure of feedback functional gains. A two di- [email protected] mensional problem is employed to illustrate the theoretical and numerical results and to demonstrate the feasibility of this method. MS59 Well-Posedness of Hyperbolic Partial Differential Weiwei Hu Equations on the Semiaxis University of Southern California [email protected] Hyperbolic partial differential equations on the semiaxis are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of MS58 non-homogeneous transmission lines on the semiaxes. The Shape Optimization for Second-Order Systems main result of this talk is a simple test for C0-semigroup generation in terms of the boundary conditions at the point Modern materials mean that it is possible to provide pas- zero. The results are illustrated with several examples. sive damping for vibrations. Consider choosing viscous damping in abstract second-order systems; that is choose Birgit Jacob d(x)in Universität Wuppertal, Germany [email protected] w¨(x, t)+Aow(x, t)+d(x)Iw˙ (x, t)=0 Sven-Ake Wegner where Ao is a non-negative self-adjoint operator. The moti- University of Wuppertal vating example is a vibrating beam or string where patches [email protected] are placed to increase viscous damping. Optimal damping in a vibrating string has been studied by many researchers; for instance Cox and Zuazua (1994), Fahroo and Ito (1997), MS59 Hébrard and Henrot (2005), Privat et al (2013). The ap- Strong Stabilization of the SCOLE Model using a proach of Morris (2011) is extended to obtain new results, Tuned Mass Damper which also apply to first order systems. It is shown that minimization of a quadratic cost functional is appropriate We study the vibration reduction of the non-uniform for maximization of the decay rate. The existence of an SCOLE (NASA Spacecraft Control Laboratory Experi- optimal actuator location depends on the continuity of the ment) model representing a vertical beam clamped at the generator with respect to d. The results are illustrated with bottom, with a rigid body having a large mass on top, us- simulations. ing a Tuned Mass Damper (TMD). The TMD is a heavy trolley mounted on top of the rigid body, connected to the Kirsten Morris, Ambroise Vest rigid body via a spring and a damper. Such an arrange- Dept. of Applied Mathematics ment is used to stabilize tall buildings. Using our recent University of Waterloo well-posedness and strong stabilization results for coupled [email protected], [email protected] impedance passive linear time-invariant systems (possibly infinite-dimensional), we show the following: The SCOLE system with the trolley is well-posed and regular on the MS59 energy state space with the force or torque acting on the Towards Moment Matching of a Perturbed Wave rigid body as input and with the speed or angular velocity PDE of the rigid body as output, and this system is strongly stable on the energy state space. Finite-dimensional approximations of partial differential equations are used not only for simulation, but also for Xiaowei Zhao controller design. The model reduction technique we use is School of Engineering the so-called time-domain moment matching method. The University of Warwick idea is that the steady-state response of the approximant [email protected] when excited by some specific input signal matches the steady-state response of the given model, when excited by George Weiss the same input. The result of applying this method is a School of Electrical Engineering family of parameterized approximations which contains a Tel Aviv University wide variety of models suitable for different goals. We are [email protected] going to exploit this asset for boundary control systems and explore it for a particular fractional system, namely a perturbed wave equation. MS59 Orest Iftime Waves: Observation, Control and Numerics Department of Economics and Econometrics We present a recent result on numerical approximation of University of Groningen boundary-controlled wave equations. When the wave equa- [email protected] tion is discretized, most numerical schemes produce high frequency wave packets with null group velocity that do Tudor Ionescu not reach the boundary, and accordingly cannot be con- University of Sheffield trolled. We construct a suitable non-uniform grid, such Departmen of Automatic Control and Systems that controllability is ensured uniformly on the mesh size Engineering parameter. This allows ensuring the convergence of the nu- t.ionescu@sheffield.ac.uk merical approximations of the boundary controls without added filtering mechanisms. Denis Matignon ISAE-Supaero, University of Toulouse Enrique Zuazua 122 CT15 Abstracts

Ikerbasque & Basque Center for Applied Mathematics [email protected] (BCAM [email protected] MS60 Quasi-stationary Approximation and Shadow Limit MS59 for Reaction-diffusion-ode Models of Biological Pattern Formation using Renormalisation Group Exponential Stabilization of Boundary Controlled Method Linear Port Hamiltonian Systems with Non-linear Dynamic Control The talk is devoted to reduction of multiscale reaction- diffusion-ode models. Such systems of equations arise, for example, from modeling of interactions between diffusing Exponential stability of boundary controlled port- signaling factors and processes localized in cells and on cell Hamiltonian systems defined on a one-dimensional spatial membranes. We propose a rigorous approach based on the domain with non-linear dynamic boundary controller is ad- renormalisation group (RG) approximation of singularly dressed. For a finite-dimensional controller it is shown that perturbed equations. We consider various scalings which the closed-loop system possesses unique solutions, and that lead to quasi-stationary approximation or shadow limits. exponential stability can be obtained. This result follows Applicability of the reduced models to study dynamics of by regarding the closed-loop system as a linear boundary pattern formation is discussed on several examples from control system subject to a Lipschitz continuous non-linear mathematical biology. perturbation at its boundary. By estimating the decay of energy exponential stability is proved. Anna Marciniak-Czochra University of Heidelberg Hans Zwart Germany Department of Applied Mathematics [email protected] University of Twente [email protected] MS60 Yann Le Gorrec, Hector Ramirez Upscaling of Interaction of Flow, Chemical Reac- FEMTO-ST AS2M, ENSMM tions and Deformation in Heterogenous Media [email protected], [email protected] Experimental research on deformable porous media, like living tissues, is providing more and more detailed information on the nano- and micro-scale and this talk we will MS60 present mathematical modeling of reactive flow and trans- Homogenization of a Precipitation-dissolution port and its interaction transport through tissue under Model in a Porous Medium varying mechanical and chemical conditions. Here we consider equations on the fine scale modeling the real processes occurring in the deformable pore space, in the solid struc- We employ homogenization techniques to provide a rigor- ture and in the interfaces (membranes). We are including ous derivation of the Darcy scale model for precipitation and dissolution in porous media. The starting point is the 1. Fluid flow and diffusion, transport and reactions of pore scale model which is a coupled system of evolution the substances it transports. equations involving a parabolic equation. This models ion 2. Exchange of fluid and substances at the interfaces. transport in the fluid phase of a periodic porous medium Small deformation of the solid structure. and is coupled to an ordinary differential equations mod- 3. Changes of the structures and their mechanical prop- eling dissolution and precipitation at the grains boundary erties with the flow and with the substances concen- (van Duijn and Pop (2004)). The main challenge is in trations. dealing with the dissolution and precipitation rates, which involve a monotone but multi-valued mapping. In order Our goal is to obtain the upscaled system modeling re- to pass to the limit in these rate functions at the bound- active flow through biological tissues on the macroscopic ary of the grains, we prove strong two scale convergence scale, starting from a system on the pore level. Using mul- for the concentrations at the microscopic boundary and tiscale techniques, we preform the scale limit and derive use refined arguments in order to identify the form of the a macroscopic (effective) model system, preserving rele- macroscopic dissolution rate, which is again a multi-valued vant information on the processes on the microscopic level. function. The resulting upscaled model is consistent with One obtains in the limit a system similar to the quasi- the Darcy scale model formally proposed in van Duijn, Kn- static Biot-law but coupled with chemical reactions. Using abner, Hengst (1995). the characteristic time scalings resulting from the analysis of the real data, we will undertake further analysis and Kundan Kumar show how the mechanics could be decoupled from the re- University of Texas, Austin active flows. The modeling novelty in our paper is depen- [email protected] dence of the Young modules, of the elastic structure, on the concentration. Consequently, the reactive flows causes the deformation. Adding diffusion, transport and reactions Maria Neuss-Radu of chemical substances and their interaction to mechanics University of Erlangen-Nuremberg leads to new mathematical difficulties requiring new ideas Mathematics Department and methods. In addition to the formal upscaling, we will [email protected] give some hints about the rigorous homogenization result. Sorin Pop CASA Andro Mikelic Eindhoven University of Technology Institut Camille Jordan, Departement de Mathématiques CT15 Abstracts 123

Universit´eLyon1 Ulrich Koehler [email protected] Hella KGaA Hueck & Co. [email protected]

MS60 Sina Ober-Bloebaum, Sebastian Peitz Capturing Secondary Nucleation Effects in Becker- University of Paderborn Doering Interactions: The Homogenization Route [email protected], [email protected] We present a continuum PDE-ODE model for collagen self- assembly describing the interplay between the change in Sebastian Tiemeyer the polymer distribution and the evolution of monomers. Hella KGaA Hueck & Co. We endow the model with periodic coefficients, where the [email protected] small parameter is interpreted in this context as the ratio of lengths of monomers and fibrils. After applying a fixed- point homogenization argument and proving corrector es- MS61 timates, we use the microscopic information incorporated Integrated Building Energy Management: Current in the first-order correctors to explain the so-called tur- State and Key Technology Challenges bidity measurement. Finally, we compare qualitatively our multiscale modelling, mathematical analysis, and simula- This presentation will outline the current key research and tion results with experimental data. This work is a joint demonstration activities of UTRC in the area of building collaboration with B. van Lith and C. Storm (Eindhoven). energy management including two main demonstration ef- See [B.S. van Lith, A. Muntean, A. Muntean: A continuum forts on buildings and HVAC modelling and control cur- model for hierarchical fibril assembly. Europhysics Letters rently undertaken in the US and Ireland. The presentation (EPL), 106 (2014), 08004.¡http://iopscience.iop.org/0295- will highlight the key challenges and research opportunities 5075/106/6/68004] and [O. Krehel, T. Aiki, A. Muntean: for the applied mathematics community that will drive the A thermo-diffusion system with Smoluchowski interactions: mini-symposium discussion. well-posedness and homogenisation. Networks and Hetero- geneous Media 9(2014), 4, 739-762] for further reading. Konstantinos Kouramas United Technologies Research Center Ireland Adrian Muntean [email protected] Department of Mathematics and Computer Science TU Eindhoven Draguna Vrabie [email protected] United Technologies Research Center [email protected]

MS61 Marcin Cychowski, Stevo Mijanovic Multiobjective Optimal Control Techniques in En- United Technologies Research Center Ireland ergy Management [email protected], [email protected]

We present a numerical set-oriented technique for the solution of multiobjective optimal control problems. First, the MS61 problem is transformed into a classical nonlinear multiob- Scheduling of Multi Energy Systems: Do We Re- jective optimization problem by an appropriate discretiza- ally Need a Global Optimum? tion of the control. Then, the entire Pareto set is computed using both global subdivision and continuation methods. The definition of the optimal scheduling of a multi-energy The functionality of the different algorithms is compared system is in general a very complex and computational in- and illustrated by the optimization of energy consumption tensive process. On the other hand, models and inputs and temporal performance of an electric drive. to the optimization are affected by significant uncertainty. Starting from these considerations, the paper analyses the Michael Dellnitz role of optimality versus the role of flexibility and robust- University of Paderborn ness of the solution. Theoretical considerations are com- [email protected] bined with real life experience in the optimization of different real city quarters.

Julian Eckstein Antonello Monti Hella KGaA Hueck & Co. E.ON Energy Research Center - RWTH Aachen [email protected] University [email protected] Kathrin Flasskamp University of Paderborn Dirk Mueller, Rita Streblow [email protected] RWTH Aachen University [email protected], [email protected] Patrick Friedel aachen.de Hella KGaA Hueck & Co. [email protected] MS61 Christian Horenkamp Fault Tolerant Control of Hvac Systems for Energy Chair of Applied Mathematics Eﬃcient Buildings University of Paderborn [email protected] System-level or operational faults in building Heating Ven- 124 CT15 Abstracts

tilation and Air Conditioning (HVAC) systems, can have Dijon significant impact on the desired and expected building en- [email protected] ergy performance and user comfort. Fault-tolerant control systems is characterized by its capability, after fault occur- rence, to recover performance close to the nominal desired MS62 performance. In this paper a method for fault decoupling Periodicity in Infinite Horizon Problems of Opti- in dynamic systems is presented. In an integrated design, mal Harvesting the proposed approach is composed of two stages : The first step is the detection and isolation of the fault based We investigate if the optimal harvesting of single species on the generation of directional residuals while the second on the infinite horizon can be proper periodic (a question step is represented by the reconfiguration mechanism which intensively discussed among practitioners). Two alterna- consists in the estimation of new control parameters after tive optimality concepts are used for a given objective in- evaluation of the performance degradation. tegrand: average revenue and discounted total revenue. We show that proper (asymptotically) periodic optimal solu- Dominique Sauter tions may appear if the heterogeneity of the species with Research Center for Automatic Contro, University of respect to age is taken into account. The analysis involves Lorraine a ”properness test” for the averaged problem and estab- [email protected] lished relations between the two problems.

Vladimir M. Veliov, Anton Belyakov MS62 Vienna University of Technology Pontryagin Principles for Systems Governed by [email protected], [email protected] Functional Diﬀerential Equations

We present a new proof of Pontryagin principle for finite MS62 and infinite horizon nonlinear problems which are governed by a functional differential equation. Structure of Extremals of Variational Problems in the Regions Close to the Endpoints Joël Blot University Paris 1 We study the structure of approximate solutions of au- [email protected] tonomous variational problems on large finite intervals. In our research which was summarized in Zaslavski, Turnpike properties in the calculus of variations and optimal control, MS62 Springer, New York, 2006 we showed that approximate so- Infinite-Horizon Multiobjective Optimal Control lutions are determined mainly by the integrand, and are Problems for Bounded Processes essentially independent of the choice of time interval and data, except in regions close to the endpoints of the time Infinite-horizon multiobjective optimal control problems interval. In the present talk we study the structure of ap- for bounded processes are studied in the discrete time case. proximate solutions in regions close to the endpoints of the These problems are governed by difference equations or in- time intervals. equations. The results generalize to the multiobjective case results obtained for singleobjective optimal control prob- Alexander Zaslavski lems in that framework. Necessary conditions and suffi- The Technion Israel Institute of Technololy cient conditions of Pareto optimality are provided namely [email protected] Pontryagin maximum principles in the strong form and in the weak form. MS63 Naila Hayek An Approximate Controllability Result with Con- Laboratoire ERMES, University Pantheon Assas Paris 2. tinuous Spectrum: the Morse Potential with Dipo- 12 place du Panthéon. 75005 Paris lar Interaction [email protected] This note presents a positive approximate controllability result for a bilinear quantum system modelling a chemical MS62 bond. The main difficulties are due to the presence of a On the Convexity of the Value Function for A Class continuous spectrum part for the uncontrolled Hamiltonian of Nonconvex Variational Problems: Existence and (modelled by a Morse potential) and the unboundedness of Optimality Conditions the interaction potential (dipolar interaction). Our proof uses averaging theory and spectral analysis. We study a class of perturbed constrained nonconvex variational problems depending on either time/state or Nabile Boussaid time/state’s derivative variables. Its (optimal) value func- Department de Mathematiques tion is proved to be convex and then several related prop- Universite de Franche Comte erties are obtained. Existence, strong duality results and [email protected] necessary/sufficient optimality conditions are established. Moreover, via a necessary optimality condition in terms of Mordukhovich’s normal cone, it is shown that local minima Marco Caponigro are global. Such results are given in terms of the Hamil- CNAM, Paris tonian function. Finally various examples are exhibited [email protected] showing the wide applicability of our main results. This a joint work with F. Flores-Bazan and G. Mastroeni. Thomas Chambrion Institut Elie Cartan Abderrahim Jourani Université de Lorraine CT15 Abstracts 125

[email protected] based on discrete-time time-consistent Markov measures and their dual representation. A general constructions as well as several particular cases will be discussed. MS63 Inverse Problems in Quantum Control in Presence Darinka Dentcheva of Uncertainties and Perturbations Department of Mathematical Sciences Stevens Institute of Technology The inversion problem of recovering the Hamiltonian and [email protected] dipole moment is considered in a quantum control framework. The inversion process uses as inputs some measurable quantities (observables) for each admissible control; MS64 however the implementation of the control is noisy (the On Stationary Markov Perfect Equilibrium in a perturbations are additive constants in a countable set of Risk-Sensitive Dynamic Stochastic Decision Model values) and therefore the data available is only in the form of the law of the measured observable. Nevertheless it is A stochastic dynamic choice model with the quasi- proved that the inversion process still has unique solutions hyperbolic discounting is analysed. WIthin such a frame- (up to some phase factors). Numerical illustrations sup- work agents preferences may hinge on time. This require- port the theoretical results. ment, in turn, leads to a non-cooperative inﬁnite horizon stochastic game played by a countably many selves repre- Ying Fu senting him during the play. A novel feature in our ap- Universit´e Paris Dauphine proach is an application of the entropic risk measure to [email protected] calculating agent’s utility. As a result, we provide theorems on the existence of Markov perfect equilibria.

MS63 Anna Jaskiewicz Controllability of the Schrödinger Equation with Institute of Mathematics and Computer Science Three Inputs Via Adiabatic Techniques Wroclaw University of Technology [email protected] In this talk we will present a constructive method to control the bilinear Schrödinger equation by means of three controlled external fields. This method can be used for in- Andrzej Nowak stance to control the electromagnetic Schrödinger equation University of Zielona Gora with three controlled (electromagnetic) potentials. The [email protected] method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersec- MS64 tions, with respect to variations of the controls, and if the latter are conical. Risk-Averse Control of Discrete-Time Markov Sys- tems Paolo Mason cnrs We shall discuss fundamental questions of modeling risk in [email protected] dynamical systems and discuss the property of time consistency and the resulting interchangeability in optimal con- Francesca Chittaro trol models. Special attention will be paid to discrete-time LSIS, UniversitédeToulon Markov systems. We shall refine the concept of time consis- [email protected] tency of risk measures for such systems, introducing conditional stochastic time consistency. We shall also introduce the concept of Markov risk measures and derive their struc- MS63 ture. This will allow to derive a risk-averse counterpart of Ensemble Controllability: Recent Results and Ap- the dynamic programming equation. Finally, we shall re- plications to Quantum Inversion view solution methods and present some examples.

The controllability of bilinear systems in presence of per- Andrzej Ruszczynski turbations is discussed. We give first some recent results Rutgers University concerning the ensemble controllability of collection of bi- [email protected] linear systems on connected, compact, simple Lie groups. The theoretical results are then applied to the controllability of collection of perturbed systems with perturba- MS64 tions being constant on at least on some common inter- A Risk-Averse Analog of the Hamilton-Jacobi- val. The circumstance of more general perturbations (time- Bellman Equation dependent stochastic random processes) is also discussed. We introduce the concept of continuous-times risk measure Gabriel M. Turinici for diffusion process. The risk-averse control problem is es- CEREMADE Université Paris Dauphine tablished via FBSDE (forward-backward stochastic differ- [email protected] ential equation) system. We derive the dynamic programming principle and prove the value function is a viscosity solution of the risk-averse Hamilton-Jacobi-Bellman equa- MS64 tion. We also discuss the approximation scheme when the Risk-Averse Control of Continuous-Time Markov classical solution exists. Chains Andrzej Ruszczynski We consider continuous time Markov process and design Rutgers University time-consistent risk measurement. The construction is [email protected] 126 CT15 Abstracts

Jianing Yao tems Operations Research Program Rutgers University The novel anti-lock brake algorithm is suggested. The al- [email protected] gorithm is based on constrained extremum searching feedback via the second order sliding mode. The algorithm allows to combine anti-lock brake system or traction system MS65 with yaw antiskid control. Convergence and stability of the Data-Driven Modeling and Control of Complex closed loop is proved via multimodal Lyapunov function. Systems: Sparse Sensing and Machine Learning The yaw control algorithm developed gives additional margins of vehicle stability during adverse driving maneuvers Abstract not available. over a variety of road conditions.

Steven Brunton Sergey Drakunov University of Washington Department of Physical Sciences [email protected] Embry-Riddle Aeronautical University, Daytona Beach, FL 3211 MS65 [email protected] Self-Tuning Electromagnetic Systems

Abstract not available. MS66 Yakubovich’s Oscillations in Systems with Discon- J. Nathan Kutz tinuous Nonlinearities University of Washington Dept of Applied Mathematics Sufficient conditions of attracting limit cycle existence for [email protected] a linear system with sign nonlinearity are discussed. It is assumed that the linear part of the system is stabiliz- able by an output feedback, the nonlinearity has linear MS65 negative term plus positive one proportional to the out- On Discovering Coherent Spatial-Temporal Modes put sign. Conditions of oscillation existence in the sense of from State and Control Input Histories with Spe- Yakubovich for this class of systems are also presented. cial Emphasis on Infectious Disease Systems Denis Efimov Abstract not available. INRIA Lille-Nord Joshua L. Proctor 59650 Villeneuve d’Ascq - France Institute for Disease Modeling denis.efi[email protected] [email protected] Andrey Polyakov INRIA Lille-Nord MS65 59650 Villeneuve d’Ascq France Enhancing Data-Driven Koopman Spectral Analy- [email protected] sis using Machine Learning Approaches Wilfrid Perruquetti In recent years, Koopman spectral analysis has become a Ecole Centrale de Lille, INRIA Lille Nord Europe popular tool for the decomposition and study of nonlinear [email protected] systems. We will discuss methods that blend ideas from machine learning with Koopman-based analyses including a kernel reformulation of Extended Dynamic Mode De- MS66 composition (Extended DMD), which is a generalization of Dynamic Mode Decomposition. We will apply these tech- A Bifurcation Approach to Locate Stable Limit Cy- niques to both numerically generated data, where their ac- cles in Nonlinear Switched Systems and Its Appli- curacy can be quantified, and to experimentally obtained cation to Anti-Lock Braking Systems data from fluid dynamics. If a switched system switches between nonlinear systems, Matthew O. Williams then deriving effective criteria for the existence and stabil- Program in Applied and Computational Mathematics ity of limit cycles is a difficult problem. Due to compli- Princeton University cate friction characteristics the anti-lock braking systems [email protected] (ABS) are essentially nonlinear. In this talk I propose a new approach where the limit cycle of a switched system Clarence Rowley (akin the ABS) is obtained as a bifurcation from a switched Princeton University equilibrium when a suitably designed parameter crosses the Department of Mechanical and Aerospace Engineering bifurcation value. [email protected] Oleg Makarenkov I. G. Kevrekidis University of Texas at Dallas Princeton University [email protected] [email protected] MS66 MS66 Hybrid Anti-Lock Braking System Algorithms and Sliding Mode Control for Anti-Lock Braking Sys- Switched Extended Braking Stiffness Observers: CT15 Abstracts 127

Two Tools for Modern Braking Systems [email protected]

We consider a class of anti-lock brake algorithms based on wheel-deceleration thresholds, for which we analyze the PP1 stability of limit cycles using the Poincar map. We also Outer Synchronization of Networks with Mobile consider the observation of an unmeasured variable called Robots XBS. We propose an observer design based on Burckhardt’s tire model. The observer’s convergence is analyzed using In this work, outer synchronization of coupled networks tools for switched linear systems. Both experiments and with non-identical topology is reported. In particular, simulations confirm the convergence properties predicted outer synchronization in nearest-neighbor and small-world by our theoretical analysis. networks with coupled mobile robots is achieved by using complex systems theory. By means of extensive numeri- William Pasillas-Lépine cal simulations we show the advantages in outer synchro- CNRS Ecole Superieure d’Electricite SUPELEC - Univ nization of small-world networks against nearest-neighbor Paris-Sud networks. Different cases of interest are studied for a large 3 rue Joliot-Curie, 91192, Gif-sur-Yvette cedex, France number of mobile robots as nodes, including network syn- [email protected] chronization without master mobile robot, and synchronization of networks with different master-slave configurations. MS67 Adrian Arellano-Delgado Control and Stabilization of Degenerate Wave Electronics and Telecommunications Department, Equations Scientific Research and Advanced Studies of Ensenada [email protected] The control of degenerate PDE’s arise in many applications such as cloaking (building of devices that lead to invisibil- Cesar Cruz-Hernandez ity properties from observation), climatology, population Electronics and Telecommunications Department, genetics, and vision. For such equations, the diffusion op- Scientific erator degenerates on some subset of the spatial domain. Research and Advanced Studies of Ensenada We shall present some recent results on observability, con- [email protected] trol and stabilization of degenerate wave equations. This is a joint work with Piermarco Cannarsa (University di Roma Tor Vergata, Italy) and Gunter Leugering (Friedrich- Rosa Martha Lopez-Gutiérrez Alexander-Universitat Erlangen-Nurnberg, Erlangen, Ger- Faculty of Engineering Architecture and Design, many). Baja California Autonomous University [email protected] Fatiha Alabau Université de Lorraine, France PP1 [email protected] A Novel Equation Error for Direct Adaptive Con- trol for a Class of First Order Systems with Exter- MS67 nal Disturbances Optimal Control on Reducing Carbon Emission A novel equation error for direct adaptive control for a class of first order systems, is studied in this paper. It is shown Abstract not available. that the Output Error, Equation Error and the proposed equation error have different convergence speeds, transient Jin Liang response characteristics and the system robustness. Simu- Tongji University lation results are used to show that the proposed equation Shanghai, China error is very much powered in disturbance rejection and Liang [email protected] has less transient time oscillations.

Yaghoub Azizi MS67 Department of Electrical Engineering Shahid Beheshti University Title Not Available - Souplet [email protected] Abstract not available. Alireza Yazdizadeh Philippe Souplet Department of Electrical Engineering LAGA, Institut Galil´ee, Universit´e Paris 13 Shahid Abbaspour University [email protected] [email protected]

PP1 MS67 Fractional Order Pid Controller Design for Mecha- On An Optimal Control Problem Arising from In- tronic Systems duction Heating In this paper is described the general framework of frac- Abstract not available. tional order PID controller parameter tuning. The method is exempliﬁed for two typical, basic models from mecha- Hong-Ming Yin tronic: the mass-spring-damper system and a benchmark Washington State University system consisting of a DC motor, a gearbox, an elastic 128 CT15 Abstracts

shaft and a load. The simulation results highlight the ad- bination of partial differential equations and ordinary dif- vantages of the method. ferential equations. The proposed observer is based on sliding mode that provides robustness to possible mismatches Roxana Both between the system model and the actual system. A for- Technical University of Cluj-Napoca mula for the observer gain is derived that guarantees sta- [email protected] bility and convergence of the distributed observer state to the actual system state. Several examples are considered Dulf Eva, Muresan Cristina that illustrate the approach. Technical University of Cluj Napoca [email protected], [email protected] Niloofar N. Kamran Embry-Riddle Aeronautical University [email protected] PP1 Synchronization of Mobile Robots in Deterministic Sergey Drakunov Small-World Networks Department of Physical Sciences Embry-Riddle Aeronautical University, Daytona Beach, This work presents the network synchronization of cou- FL 3211 pled mobile robots in deterministic small-world networks. [email protected] Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. It is known to us all, stochasticity is a common feature PP1 of complex network models that generate small-world and A Novel Tuning Method for Fractional Order Pid scale-free topologies. In particular, we consider determinis- Controller tic small-world networks created by edge iterations, i.e. the networks are growing due to deterministic algorithm. The The idea of the magnitude optimum method is to find a network synchronization is achieved by using complex sys- controller that makes the frequency response from refer- tems theory, in which, for all reported case studies, we ob- ence to plant output as close as possible to unity for low tain synchronization of deterministic small-word networks frequencies. However, the method is not frequently used by using the same coupling strength. That is, the increase in practice being sensitive to modeling errors. A novel of mobile robots in the deterministic networks does not approach is proposed in this work, using fractional order affect the synchronization condition. controllers, recognized for their robustness to plant gain variations. The case study is the pilot plant of 13Csepa- Rosa Martha Lopez-Gutierrez ration. Universidad Autonoma de Baja California [email protected] Eva H. Dulf, Cristina Muresan, Roxana Both Technical University of Cluj-Napoca Rigoberto Mart´ınez-Clark, Daniel Reyes-De La Cruz, [email protected], [email protected], rox- Cesar Cruz-Hernández [email protected] CICESE [email protected], [email protected], PP1 [email protected] On Dynamics of Current-Induced Static Wall Pro- files in Ferromagnetic Nanowires Governed by the PP1 Rashba Field Clustering Methods for Control-Relevant Decom- This article deals with the analytical study of propagation position of Complex Process Networks of static wall profiles in ferromagnetic nanowires under the effect of spin orbit Rashba field. We consider the govern- Complex process networks are ubiquitous in chemi- ing dynamics as an extended version of Landau-Lifshitz- cal/energy plants, and typically cannot be controlled ef- Gilbert equation of micromagnetism which comprise the fectively via purely decentralized control approaches. We nonlinear dissipation factors like dry-friction and viscous. consider the identification of constituent sub-networks such We establish threshold and Walker-type breakdown esti- that the components of each network are strongly con- mates for the external sources in the steady regime and nected whereas different sub-networks are weakly con- also illustrate the obtained results numerically. nected. We propose a hierarchical clustering method to generate manipulated input/controlled output clusters of Sharad Dwivedi, Shruti Dubey varying modularity, using relative degree information to Indian Institute of Technology Madras define appropriate notions of distance (closeness) between [email protected], [email protected] such clusters and compactness within clusters.

Prodromos Daoutidis PP1 University of Minnesota Construction of Hybrid Decision Processes Dept. of Chemical Engineering and Materials Science [email protected] In the real world, we often encounter the complex phenomena which could not be analyzed only by probability theory. In order to overcome this diﬃculty, Li and Liu PP1 have proposed chance theory. In this paper we consider a Observer Design for Distributed Parameter Sys- method of constructing of a Markov-type hybrid process tems from stochastic kernel and credibilistic kernel and give the existence and the property of optimal policies. In this paper we suggest a novel design of a nonlinear observer for distributed parameter system described by com- Masayuki Kageyama CT15 Abstracts 129

Nagoya City University University of Western Ontario [email protected] [email protected], [email protected]

PP1 PP1 Title Not Provided - Kasimova Feedback Stabilization of a Fluid-Structure Model: Theory and Numerics. Randomly generated control of insects motion experimentally studied in formicarium and by mathematical model We study the stabilization of the Navier-Stokes equations of ants foraging paths from nest to food locus [1]. Paths in 2D around an unstable stationary solution. The config- are impeded by barriers , viz. segments of given size, ran- uration corresponds to a flow around a bluff body. Two domly centered-oriented with respect to nest-food straight beams are located at the boundary of the body and their line. When insects collide with the obstacle the trajectory deformations are used to stabilize the flow. The control bifurcates and the branch making an acute angle with the is a force in the beam equations. We study theoretically smell gradient is selected. Trajectories consists of 1 or 3 and numerically the feedback stabilization of this system components. Space-realizations average travel time is eval- coupling the Navier-Stokes equations with the beam equa- uated. tions.

Rouzalia Kasimova Moctar Ndiaye,MichelFournié German University of Technology in Oman Institut de Mathématiques de Toulouse [email protected] [email protected], [email protected] Denis Tishin Kazan Federal University, Russia Jean-Pierre Raymond [email protected] Universite’ Paul Sabatier, Toulouse [email protected] Yurii Obnosov Kazan Federal University, Russia Institute of Mathematics and Mechanics PP1 [email protected] Robustified H2-Control of a System with Large State Dimension

PP1 We consider the design of an output feedback controller Model-Free Optimal Tracking Control Via Nuclear for a large scale system like the linearized Navier-Stokes Norm Minimization equation. We design an observer-based controller for a reduced system that achieves a compromise between concur- Model-based control is a two step procedure: 1) a model ring performance and robustness specifications. This con- of the plant is identified from data, 2) a controller is syn- troller is then pulled back to the large scale system such thesized using the model. Model-free control aims to find that closed-loop stability is preserved, and such that the the control signal directly from the data. We show that trade-off between the H2-andH∞-criteria achieved in re- model-free control is equivalent to Hankel structured low- duced space is preserved. The procedure is tested on a rank matrix approximation and completion. The missing simulated fluid flow study. data in the matrix formulation is the to-be-found control signal and the approximation is the tracking error. Nu- Laleh Ravanbod clear norm relaxation is used for numerical solution of the Institut de Mathématiques de Toulouse, France problem. [email protected]

Ivan Markovsky Dominikus Noll Vrije Universiteit Brussel (VUB) Universite Paul Sabatier [email protected] Institut de Mathematiques [email protected] PP1 Jean-Pierre Raymond Extension of the Sethi Model to the Advertising of Universite’ Paul Sabatier, Toulouse Digital Products [email protected] In this paper, a model is formulated that modifies the Sethi model of advertising optimization to incorporate unique Jean-Marie Buchot features present in the mobile game space. Although the Institut de Mathématiques de Toulouse, France optimization of advertising in traditional industries has [email protected] been thoroughly studied, the optimization models used lack sufficient predictive power for several emerging market sec- tors. For the free-to-play video game industry in particular, PP1 there are issues that arise in the form of uncertain revenue Design of a Soft Sensor Based on Neural Networks from users and the effect of the ranking systems used for for the Estimation of High Differential Pressure on these games. This paper compares the modified and origi- High Temperature Shift Catalyst in Ammonia Pro- nal Sethi models and it is shown how little or no advertising duction Plants in the video game industry can still result in a large market share given sufficient virality parameters for the game. The ammonia production plants use to experience an incre- ment of the differential pressure across the High Temper- Alex D. Murray, Allan MacIsaac ature Shift (HTS) catalyst. This issue results in reduced 130 CT15 Abstracts

ammonia production due to a continuous plant rate reduc- Disturbances tion to accommodate the increasing pressure and also a solid waste formation. An alternative method for monitor- This paper proposes a novel adaptive backstepping sliding the pressure is a soft sensor based on in neural networks. ing mode control methodology for an X-Y high precision In the present work, a neural network has been design and servo manipulation system. The control methodology is training relating the pressure (output) with a set of the proposed for tracking desired motion trajectories in the process variables and kinetic of the reaction. The results presence of unknown system parameters, input saturations, indicated an accuracy of 4%. A soft control system based and external disturbances. In this study, an auxiliary on the neural network has been found to substantially good structure is employed to analyze the effect of input sat- for the reduction of pressure fluctuations. This kind of sys- urations, by which the proposed control scheme is success- tem can be used to prevent the same problem in any other fully designed to achieve a high tracking performance in the similar ammonia plants. presence of the aforementioned conditions. The stability of the closed-loop system is analyzed and the proposed con- Carmen Riverol trol architecture is tested in real-time experiments. Finally, chemical engineering simulation results and experimental results are provided to [email protected] illustrate the effectiveness of the proposed criteria.

Vashti Goorahlal Peng Yan Chemical Engineering Department Beihang University University of the West Indies [email protected] [email protected] Yangming Zhang Beihang University PP1 China Bioeconomic Analysis Supports the Endangered [email protected] Species Act Zhen Zhang The Endangered Species Act (ESA) was enacted to re- Tsinghua University store declining natural populations. The ESA mandates China species protection irrespective of costs; this translates to [email protected] restriction of activities harming endangered populations. We discuss criticisms of the ESA in the context of public land management and examine under what circumstance banning non-conservation activity on multi-use lands can be socially optimal. We develop a bioeconomic model to frame the management problem and identify scenarios where ESA-imposed regulation is optimal.

Kehinde R. Salau The University of Arizona [email protected]

Eli Fenichel Yale University [email protected]

PP1 Optimal Identiﬁcation of Distributed System

We seek to find effective identification algorithms for a system that involves a set of spatially distributed sensors and a fusion center. The sensors make local observations which are noisy versions of a signal of interest. Each sensor trans- mits compressed information about its measurements to the fusion center which should recover the original signal within a prescribed accuracy. The key problem is to identify models of the sensors and the fusion center. We show how the required models follow from the solution of the associated least squares problems.

Anatoli Torokhti University of South Australia School of Information Technology & Mathematical Sciences [email protected]

PP1 Controller Design for High Precision Servo Sys- tems with Model Uncertainties, Saturations and