50 CT15 Abstracts

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 ma- trices 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 differ- ence, 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 Técnica 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

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