DOCSLIB.ORG

Linköping University Postprint

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Linköping University Postprint Linköping University Postprint A Basic Convergence Result for Particle Filtering Xiao-Li Hu, Thomas B. Schön and Lennart Ljung N.B.: When citing this work, cite the original article. Original publication: Xiao-Li Hu, Thomas B. Schön and Lennart Ljung, A Basic Convergence Result for Particle Filtering, 2008, IEEE Transactions on Signal Processing, (56), 4, 1337-1348. http://dx.doi.org/10.1109/TSP.2007.911295. Copyright: IEEE, http://www.ieee.org Postprint available free at: Linköping University E-Press: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11748 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 56, NO. 4, APRIL 2008 1337 A Basic Convergence Result for Particle Filtering Xiao-Li Hu, Thomas B. Schön, Member, IEEE, and Lennart Ljung, Fellow, IEEE Abstract—The basic nonlinear filtering problem for dynamical where and is the func- systems is considered. Approximating the optimal filter estimate tion of the state that we want to estimate. We are inter- by particle filter methods has become perhaps the most common ested in estimating a function of the state, such as and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the the- from observed output data . An especially common oretical aspects of the quality of the approximation. Still a clear-cut case is of course when we seek an estimate of the state itself result that the approximate solution, for unbounded functions, con- , where . verges to the true optimal estimate as the number of particles tends In order to compute (3) we need the filtering probability density to infinity seems to be lacking. It is the purpose of this contribution function . It is well known that this density function to give such a basic convergence result for a rather general class of unbounded functions. Furthermore, a general framework, in- can be expressed using multidimensional integrals [1]. The cluding many of the particle filter algorithms as special cases, is problem is that these integrals only permits analytical solu- given. tions in a few special cases. The most common special case Index Terms—Convergence of numerical methods, nonlinear es- is of course when the model (2) is linear and Gaussian and timation, particle filter, state estimation. the solution is then given by the Kalman filter [2]. However, for the more interesting nonlinear/non-Gaussian case we are forced to approximations of some kind. Over the years there I. INTRODUCTION has been a large amount of ideas suggested on how to perform these approximations. The most popular being the extended HE nonlinear filtering problem is formulated as follows. Kalman filter (EKF) [3], [4]. Other popular ideas include TThe objective is to recursively in time estimate the state in the Gaussian-sum approximations [5], the point-mass filters the dynamic model, [6], [7], the unscented Kalman filter (UKF) [8] and the class of multiple model estimators [9]. See, e.g., [10] for a brief (1a) overview of the various approximations. In the current work (1b) we will discuss a rather recent and popular family of methods, commonly referred to as particle filters (PFs) or sequential where denotes the state, denotes the Monte Carlo methods. measurement, and denote the stochastic process and mea- The key idea underlying the particle filter is to approxi- surement noise, respectively. Furthermore, the dynamic equa- mate the filtering density function using a number of particles tions for the system are denoted by according to and the equations modelling the sensors are denoted by . Most applied signal processing problems can be written in the following special case of (1): (4) (2a) (2b) where each particle has a weight associated to it, and denotes the delta-Dirac mass located in . Due to the delta-Dirac with and independent and identically distributed (i.i.d.) and form in (4), a finite sum is obtained when this approximation is mutually independent. Note that any deterministic input signal passed through an integral and hence, multidimensional inte- is subsumed in the time-varying dynamics. The most com- grals are reduced to finite sums. All the details of the particle monly used estimate is an approximation of the conditional ex- filter were first assembled by Gordon et al. in 1993 in their sem- pectation inal paper [11]. However, the main ideas, save for the crucial (3) resampling step, have been around since the 1940s [12]. Whenever an approximation is used it is very important to ad- dress the issue of its convergence to the true solution and more Manuscript received March 16, 2007; revised September 11, 2007. The as- sociate editor coordinating the review of this manuscript and approving it for specifically, under what conditions this convergence is valid. publication was Dr. Subhrakanti Dey. This work was supported by the strategic An extensive treatment of the currently existing convergence research center MOVIII, funded by the Swedish Foundation for Strategic Re- results can be found in the book [13] and the excellent survey search, SSF. X.-L. Hu is with the Department of Mathematics, College of Science, China papers [14], [15]. They consider stability, uniform convergence Jiliang University, 310018 Hangzhou China (e-mail: [email protected]). (see also [16] and [17]), central limit theorems (see also [18]) T. B. Schön and L. Ljung are with the Division of Automatic Control, Depart- and large deviations (see also [19] and [20]). The previous re- ment of Electrical Engineering, Linköping University, SE–581 83 Linköping, Sweden (e-mail: [email protected]; [email protected]). sults prove convergence of probability measures and only treat Digital Object Identifier 10.1109/TSP.2007.911295 bounded functions , effectively excluding the most commonly 1053-587X/$25.00 © 2008 IEEE 1338 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 56, NO. 4, APRIL 2008 used state estimate, the mean value. To the best of our knowl- The state process is a Markov process with initial state edge there are no results available for unbounded functions . obeying an initial distribution . The dynamics, de- The main contribution of this paper is that we prove convergence scribing the state evolution over time, is modelled by a Markov of the particle filter for a rather general class of unbounded func- transition kernel such that tions, applicable in many practical situations. This contribution will also describe a general framework for particle filtering al- (6) gorithms. It is worth stressing the key mechanisms that enables us to for all , where denotes the Borel -algebra study unbounded functions in the particle filtering context. on . Given the states , the observations are conditionally 1) The most important idea, enabling the contribution in the independent and have the following marginal distribution present paper, is that we consider the relation between the function and the density functions for noises. This im- plies that the class of functions will depend on the in- (7) volved noise densities. 2) We have also introduced a slight algorithm modification, For convenience we assume that and required to complete the proof. It is worth mentioning that have densities with respect to a Lebesgue measure, allowing us this modification is motivated from the mathematics in the to write proof. However, it is a useful and reasonable modification of the algorithm in its own right. Indeed, it has previously been used to obtain a more efficient algorithm [21]. (8a) In Section II we provide a formal problem formulation and introduce the notation we need for the results to follow. A brief (8b) introduction to particle filters is given in Section III. In an at- tempt to make the results as available as possible the particle In the following example it is explained how a model in the form filter is discussed both in an application oriented fashion and in (2) relates to the more general framework introduced above. a more general setting. The algorithm modification is discussed 1) Example 2.1: Let the model be given by (2), where the and illustrated in Section IV. Section V provides a general ac- probability density functions of and are denoted by count of convergence results and in Section VI we state the main and , respectively. Then we have the following relations: result and discuss the conditions that are required for the result to hold. The result is then proved in Section VII. Finally, the (9a) conclusions are given in Section VIII. (9b) II. PROBLEM FORMULATION B. Conceptual Solution In practice, we are most interested in the marginal distribu- The problem under consideration in this work is the fol- tion , since the main objective is usually to estimate lowing. For a fixed time , under what conditions and for which and the corresponding conditional covariance. This functions does the approximation offered by the particle filter section is devoted to describing the generally intractable form converge to the true estimate of . By the total probability formula and Bayes’ for- mula, we have the following recursive form for the evolution of (5) the marginal distribution: In order to give the results in the most simple form possible we are only concerned with -convergence in this paper. The more general case of -convergence for is also under (10a) consideration, using a Rosenthal-type inequality [22]. A. Dynamic Systems (10b) We will now represent model (1) in a slightly different frame- where we have defined and as transformations between work, more suitable for a theoretical treatment. Let ( ) probability measures on . be a probability space on which two real vector-valued Let us now introduce some additional notation, commonly stochastic processes and used in this context. Given a measure , a function , and a are defined. The -dimensional Markov transition kernel , denote process describes the evolution of the hidden state of a dynamic system, and the -dimensional process denotes (11) the available observation process of the same system.
Load more

Recommended publications
  • Decentralized Particle Filter with Arbitrary State Decomposition
    Linköping University Post Print Decentralized Particle Filter with Arbitrary State Decomposition Tianshi Chen, Thomas B. Schön, Henrik Ohlsson and Lennart Ljung N.B.: When citing this work, cite the original article. ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Tianshi Chen, Thomas B. Schön, Henrik Ohlsson and Lennart Ljung, Decentralized Particle Filter with Arbitrary State Decomposition, 2011, IEEE Transactions on Signal Processing, (59), 2, 465-478. http://dx.doi.org/10.1109/TSP.2010.2091639 Postprint available at: Linköping University Electronic Press http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-66191 1 Decentralized Particle Filter with Arbitrary State Decomposition Tianshi Chen, Member, IEEE, Thomas B. Sch¨on, Member, IEEE, Henrik Ohlsson, Member, IEEE, and Lennart Ljung, Fellow, IEEE Abstract—In this paper, a new particle filter (PF) which we In this paper, a new PF, which we refer to as the decen- refer to as the decentralized PF (DPF) is proposed. By first tralized PF (DPF), will be proposed. By first decomposing the decomposing the state into two parts, the DPF splits the filtering state into two parts, the DPF splits the filtering problem of problem into two nested sub-problems and then handles the two nested sub-problems using PFs. The DPF has the advantage over system (1) into two nested sub-problems and then handles the regular PF that the DPF can increase the level of parallelism the two nested sub-problems using PFs.
    [Show full text]
  • Rune Andersson Lennart Ljung Anne-Marie Eklund Löwinder Torsten Persson
    Ingenjörer utan gränser fixar vatten i Tanzania 8 Lagförslag ska underlätta för forskare som använder register 12 IVAAKTUELLT NR 5 2018. GRUNDAD 1930 MEDALJÖRER Rune Andersson Lennart Ljung Anne-Marie Eklund Löwinder Torsten Persson Plastkulor var Bofors vapen 1950-talet – när Sverige Försenade experimentbyggen i marknadskrig om tandkräm var stort på Big science hot mot forskningen vid Max IV IVA Opinion Forskning och innovation nycklar till hållbart samhälle mfattande skogsbränder i Sverige, det. Och i mitten av 1990-talet kopplades globalt värmerekord i Afrika, krafti- pc:n ihop med internet tack vare forskare ga monsunregn i Indien och orkaner vid CERN. En av årets nobelpristagare, i USA och Filippinerna. Klimatfors- Francis Arnold, har lyckats med att utveckla kare menar att 2018 riskerar att gå metodik för att ta fram enzymer som nu Otill historien som året då global uppvärmning används för att tillverka allt från biobräns- förstärkte extremväder runt hela vårt klot och len till läkemedel. varnar: vi är på väg mot en uppvärmning med Historien upprepar sig sällan. Men den 2 grader redan om 30-50 år. lär oss att ett kunskapssamhälle ska byggas TUULA TEERI på en stabil vetenskaplig grund med lång- Men det behöver inte sluta med apo- siktiga forskningssatsningar. kalyps. Nyligen lanserades rapporten »Historien upp- ”Exponential Climate Action Roadmap”. För att forskning ska komma till nytta Den inger hopp: det investeras just nu måste resultaten spridas effektivt. Här har repar sig sällan. biljoner i fossilfri teknik. Världens vind- och svenska universitet och högskolor en stor Men den lär oss solkraft fördubblas vart fjärde år. Försiktigt utmaning.
    [Show full text]
  • Segmentation of ARX-Models Using Sum-Of-Norms Regularization✩
    ARTICLE IN PRESS Automatica ( ) – Contents lists available at ScienceDirect Automatica journal homepage: www.elsevier.com/locate/automatica Brief paper Segmentation of ARX-models using sum-of-norms regularization✩ a, a b Henrik Ohlsson ∗, Lennart Ljung , Stephen Boyd a Department of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden b Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA article info abstract Article history: Segmentation of time-varying systems and signals into models whose parameters are piecewise constant Received 24 July 2009 in time is an important and well studied problem. Here it is formulated as a least-squares problem with Received in revised form sum-of-norms regularization over the state parameter jumps, a generalization of 1-regularization. A nice 3 December 2009 property of the suggested formulation is that it only has one tuning parameter, the regularization constant Accepted 10 March 2010 which is used to trade-off fit and the number of segments. Available online xxxx © 2010 Elsevier Ltd. All rights reserved. Keywords: Segmentation Regularization ARX-models θ 1. Model segmentation A time-varying parameter estimate ˆ can be provided by various tracking (on-line, recursive, adaptive) algorithms. A special Estimating linear regression models situation is when the system parameters are piecewise constant, and change only at certain time instants tk that are more or less y(t) ϕT (t)θ (1) rare: = θ(t) θk, tk < t tk 1. (5) is probably the most common task in system identification. It is = ≤ + well known how ARX-models This is known as model or signal segmentation and is common in e.g.
    [Show full text]
  • Asymptotic Variance Expressions for Estimated Frequency Functions Liang-Liang Xie and Lennart Ljung, Fellow, IEEE
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 46, NO. 12, DECEMBER 2001 1887 Asymptotic Variance Expressions for Estimated Frequency Functions Liang-Liang Xie and Lennart Ljung, Fellow, IEEE Abstract—Expressions for the variance of an estimated fre- where the spectra of and are and , respectively. quency function are necessary for many issues in model validation Then the basic result is that the variance of the estimated fre- and experiment design. A general result is that a simple expression quency function is given by for this variance can be obtained asymptotically as the model order tends to infinity. This expression shows that the variance is inversely proportional to the signal-to-noise ratio frequency by (3) frequency. Still, for low order models the actual variance may be quite different. This has also been pointed out in several recent publications. In this contribution we derive an exact expression where the expression is asymptotic in both the model order , for the variance, which is not asymptotic in the model order. This and the number of data . For this result to hold, it is essentially expression applies to a restricted class of models: AR-models, only required that the model parameterization in (1) has a block as well as fixed pole models with a polynomial noise model. It brings out the character of the simple approximation and the shift structure, so that the gradient w.r.t. the parameter block , convergence rate to the limit as the model order increases. It also , is a shifted version of the gradient w.r.t. (see [7, p.
    [Show full text]
  • Ieee Control Systems Award Recipients
    IEEE CONTROL SYSTEMS AWARD RECIPIENTS 2018- JOHN TSITSIKLIS “For contributions to the theory and Clarence J. Lebel Professor of application of optimization in large dynamic Electrical Engineering, and distributed systems.” Massachusetts Institute of Technology, Cambridge, Massachusetts, USA 2017- RICHARD M. MURRAY “For contributions to the theory and Everhart Professor of Control & applications of nonlinear and networked Dynamical Systems and control systems.” Bioengineering, Caltech, Pasadena, California, USA 2016 – ARTHUR J. KRENER “For contributions to the analysis, control, Research Professor, Naval and estimation of nonlinear control Postgraduate School, Monterey, systems.” CA, USA 2015 - BRUCE FRANCIS "For pioneering contributions to H-infinity, Professor Emeritus, University of linear-multivariable, and digital control." Toronto, Toronto, Ontario, Canada 2014 – TAMER BASAR “For seminal contributions to dynamic Swunlund Endowed Chair and CAS games, stochastic and risk-sensitive Professor of Electrical and control, control of networks, and Computing Engineering, University hierarchical decision making.” of Illinois, Urbana-Champaign, Urbana, IL, USA 2013 - STEPHEN P. BOYD “For contributions to systems design and Samsung Professor of Electrical analysis via convex optimization.” Engineering, Stanford University, Palo Alto, CA USA 2012 - ALBERTO ISIDORI “For pioneering contributions to nonlinear Professor of Systems and Control, control theory.” University of Rome, Sapienza, Rome, Italy 2011 - EDUARDO D. SONTAG “For fundamental contributions to nonlinear Professor II of Mathematics, systems theory and nonlinear feedback Rutgers University control.” Piscataway, NJ USA 2010 – GRAHAM CLIFFORD GOODWIN “For contributions to the theory and Prof & Dir ARC Center of Excellence practice of digital and adaptive control.” 1 of 4 IEEE CONTROL SYSTEMS AWARD RECIPIENTS in Complex Dynamic Sys & Control Univ of Newcastle Callaghan, NSW, Australia 2009 – DAVID Q.
    [Show full text]
  • CV AB with the Aim of Developing a Fully Autonomous Heavy Vehicle for Goods Transport and Other Industrial Applications)
    CURRICULUM VITAE April 8, 2021 Professor Bo Wahlberg • Born March 1, 1959 in Norrk¨oping, Sweden. Swedish citizenship. • Family status: Married since 1983 with Carina with three children (Kristina, born 1985; Stefan, born 1987; Niklas, born 1992). Grandfather to Diana (born 2007) and Miranda (born 2011). Academic Degrees: • Master of Science, Civilingenj¨or, (Applied Mathematics), June 1983, Link¨oping University, Link¨oping,Sweden. • Licentiate of Engineering (Automatic Control), June 1985, Link¨opingUniversity, Link¨oping, Sweden. • Doctor of Philosophy (Automatic Control), June 5, 1987, Link¨opingUniversity, Link¨oping, Sweden. Supervisor: Lennart Ljung. Awards: • The Tryggve Holm scholarship from SAAB SCANIA AB, 1986, for outstanding perfor- mance as a graduate student. • "The O. Hugo Schuck Best Paper Award" of the 1986 American Control Conference, Seattle 1986. • The 1995 KTH Award for outstanding contribution to the undergraduate education pro- gram at the KTH Royal Institute of Technology. • Senior Fulbright Scholar, 1997. • IEEE Fellow for contributions to system identification using orthonormal basis functions, 2007. • Best New Application Paper Award, IEEE Transactions on Automation Science and En- gineering, 2016. • Plenary Speaker, The 35th Chinese Control Conference, 2016 • IFAC Fellow for contributions to system identification and the development of orthonormal basis function, 2019 • Best Paper Award, IEEE ICDL-EpiRob, 2020 1 Academic Appointments: • Teaching assistant at the Department of Mathematics, Link¨opingUniversity, Link¨oping, Sweden, 1981 { 1983. • Teaching assistant at the Department of Electrical Engineering, Link¨opingUniversity, Link¨oping,Sweden, 1983 { 1987. • Visiting Scholar, University of Cambridge, U.K., August { December, 1985. Host: Prof. Keith Glover. • Research Associate at the Department of Electrical Engineering, Link¨opingUniversity, Link¨oping,Sweden, June 1987 { December 1987.
    [Show full text]
  • Introducing the IFAC Major Award Winners: First in a Series
    Online ISSN 1848-3380, Print ISSN 0005-1144 ATKAFF 57(3), 846–851(2016) PHONE (+43 2236) 71 4 47 | FAX (+43 2236) 72 8 59 | E-MAIL: [email protected] www.ifac-control.org Introducing the IFAC Major No.5 Award Winners: First in a Series October 2016 Over the course of this and upcoming issues of Letters, and for the Conference Editorial Board of this Newsletter readers will have the opportunity the IEEE Control Systems Society. He is a senior IN THIS ISSUE: to learn more about the winners of the IFAC Major member of IEEE and also a member of the IFAC Introducing IFAC Major Award Awards. This month readers will learn about in- Technical Committee on Networked Systems. Winners (first in a series) augural Manfred Thoma Medal winner Ming Cao, and Nichols Medal winner Lennart Ljung.The Ma- Nichols Medal: Lennart Ljung (SE) Event Report: Advances in Auto- jor Awards will be presented at the IFAC World motive Control (AAC 2016), SE Lennart Ljung received his PhD in Automatic Con- Congress in Toulouse, FR in July 2017. Introducing IFAC Fellows 2014- trol from Lund Institute of Technology in 1974. 2017 (first in a series) The names of all IFAC Major Award winners, as After a period as a post doc at Stanford, he was well as the current citations for the 2014-2017 tri- appointed to the chair of Automatic Control in IFAC Foundation Award Call ennium, can be accessed on the IFAC website. Linköping, Sweden in 1976. He has spent periods Mechatronics Journal Handover as a visiting professor at Stanford, MIT, and Uni- Ceremony Thoma Medal: Ming Cao (NL) versity of California- Berkeley (US) and Newcastle University (Australia).
    [Show full text]
  • Identification of Nonlinear State-Space Systems From
    This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCNS.2017.2758966, IEEE Transactions on Control of Network Systems 1 Identification of Nonlinear State-Space Systems from Heterogeneous Datasets Wei Pan, Ye Yuan, Lennart Ljung, Jorge Gonçalves and Guy-Bart Stan Abstract—This paper proposes a new method to identify availability of “big data” obtained from sophisticated bio- nonlinear state-space systems from heterogeneous datasets. The logical instruments, e.g., large ‘omics’ datasets, attention has method is described in the context of identifying biochemical/gene turned to the efficient and effective integration of these data networks (i.e., identifying both reaction dynamics and kinetic parameters) from experimental data. Simultaneous integration of and to the maximum extraction of information from them. various datasets has the potential to yield better performance for Such datasets typically contain (a) data from replicates of an system identification. Data collected experimentally typically vary experiment performed on a biological system of interest under depending on the specific experimental setup and conditions. Typ- identical experimental conditions, or (b) data measured from ically, heterogeneous data are obtained experimentally through a biochemical network subjected to different experimental (a) replicate measurements from the same biological system or (b) application of different experimental
    [Show full text]
  • IFAC Newsletter Issue 5, 2001
    IFAC Newsletter Issue 5, 2001 Contents: IFAC Technical Committees and their Scopes Technical Committee on Chemical Process Control Technical Committee on Mining, Mineral and Metal Processing Technical Committee on Power Plants and Power Systems Technical Committee on Control of Biotechnological Processes Technical Committee on Fault Detection, Supervision and Safety of Technical Processes - SAFEPROCESS IFAC Professional Briefs In Memoriam – Harold Chestnut Hal’s Second Family Recipient of Georgio Quazza Medal and Nathaniel B. Nichols Medal in 2002 Papers from Control Engineering Practice, September 2001 Papers from Automatica, November & December 2001 Who is Who in Ifac IFAC Technical Committees and their Scopes In our introduction of TCs and their scopes, we present the Coordinating Committee on Systems Engineering and Management Coordinating Committee on Industrial Applications Chair: T. McAvoy USA [email protected] Technical Committee on Chemical Process Control Chair : Scope: Focuses on development of new chemical control techniques and algorithms for application in pilot and industrial sized plants. Processes of interest include all techniques used in petroleum, chemical, petrochemical, speciality chemical, pharmaceutical, food, cement, and paper & pulp industries. Considers system descriptions, component selection, sensors, and actuators as well as tuning, local control, plant- wide control, and technology transfer. C. Georgakis (USA) [email protected] Technical Committee on Mining, Mineral and Metal Processing Chair : Scope: Fosters all aspects of process control in the fields of mining, mineral processing and metal processing. Includes control theory, measurements, automation, and optimization. Includes process goals, loop design, multiple control objectives, variability minimization, uniformity control, and process design. Also addresses exploration for fossil materials, but excludes petroleum refining.
    [Show full text]
  • Ieee Control Systems Award Recipients
    IEEE CONTROL SYSTEMS AWARD RECIPIENTS 2022 – DIMITRI P. BERTSEKAS “For fundamental contributions to the Professor, School of Computing, methodology of optimization and control of Informatics, and Decision Systems uncertain and large-scale dynamical Engineering, Arizona State systems, and their dissemination through University, Tempe, Arizona, USA outstanding monographs and textbooks.” 2021 – HIDENORI KIMURA “For contributions to synthesis theory of Vice Director, Systems Innovation control systems and its applications to Center, Tokyo, Japan manufacturing devices and systems.” 2020 – ANDERS LINDQUIST “For contributions to optimal filtering, Zhiyuan Chair Professor, stochastic control, stochastic realization Shanghai Jiao Tong University, theory, and system identification.” Shanghai, China 2019 – PRAMOD KHARGONEKAR “For contributions to robust and optimal Vice Chancellor for Research and control theory.” Distinguished Professor, University of California, Irvine, California, USA 2018 - JOHN TSITSIKLIS “For contributions to the theory and Clarence J. Lebel Professor of application of optimization in large dynamic Electrical Engineering, and distributed systems.” Massachusetts Institute of Technology, Cambridge, Massachusetts, USA 2017 - RICHARD M. MURRAY “For contributions to the theory and Everhart Professor of Control & applications of nonlinear and networked Dynamical Systems and control systems.” Bioengineering, Caltech, Pasadena, California, USA 2016 – ARTHUR J. KRENER “For contributions to the analysis, control, Research Professor,
    [Show full text]
  • Curriculum Vitae of Thomas Schön
    1 Curriculum Vitae of Thomas Sch¨on Uppsala, March 2021 Work Address Home Address Uppsala University Vreta Ekv¨ag2 Department of Information Technology 755 91 Uppsala, Sweden 751 05 Uppsala, Sweden Born: Phone: +46 (0) 18 471 2594 December 25, 1977 in J¨onk¨oping,Sweden. Email: [email protected] Citizenship: Web: user.it.uu.se/~thosc112/ Swedish Academic degrees Docent in Automatic Control, Link¨opingUniversity, Sweden, 2009. Doctor of Philosophy (PhD) in Automatic Control, Link¨opingUniversity, Sweden, February 2006. Licentiate of Engineering in Automatic Control, Link¨opingUniversity, Sweden, October 2003. Master of Science in Applied Physics and EE, Link¨opingUniversity, Sweden, September 2001. Bachelor of Science in Business Administration, Link¨opingUniversity, Sweden, January 2001. Academic positions Beijer Professorship in Artificial Intelligence with the Department of Information Technology, Uppsala University, since June 2020. Professor of the Chair of Automatic Control with the Department of Information Technology, Uppsala University, since September 2013-June 2020. Associate Professor with the Division of Automatic Control, Department of Electrical Engineering, Link¨oping University, September 2008-September 2013. Assistant Professor with the Division of Automatic Control, Department of Electrical Engineering, Link¨oping University, March 2006-September 2008. PhD student with the Division of Automatic Control, Department of Electrical Engineering, Link¨opingUni- versity, December 2001-February 2006. Teaching assistant (Swedish: Amanuens) at the Division of Automatic Control, Link¨opingUniversity, Link¨oping, Sweden, August 2000-July 2001. Membership professional and academic societies Member of The Royal Swedish Academy of Engineering Sciences (IVA), since 2018. Member of The Royal Society of Sciences at Uppsala, since 2018. Fellow of the ELLIS Society, since 2019.
    [Show full text]
  • Practical Issues of System Identification - Lennart Ljung
    CONTROL SYSTEMS, ROBOTICS AND AUTOMATION – Vol. VI - Practical Issues of System Identification - Lennart Ljung PRACTICAL ISSUES OF SYSTEM IDENTIFICATION Lennart Ljung Linköping University, Sweden. Keywords: parameter estimation, model structure, input design, drift, trends, identification applications, PRBS, chirp signal, ARX models, state-space models, output-error models. Contents 1. The Framework 1.1. Starting Point 1.2. Some Typical Model Structures 1.3. Estimating the Parameters 2. The User and the System Identification Problem 2.1. The Tool: Interactive Software 3. Choice of Input Signals 3.1. Common Input Signals 3.2. Periodic Inputs 4. Preprocessing Data 4.1. Drifts and Detrending 4.2. Prefiltering 5. Selecting Model Structures 6. Some Applications Glossary Bibliography Biographical Sketch Summary System Identification concerns the problem of building mathematical models of dynamical systems. This involves a fair amount of theory and algorithms. Equally important, though, is the practical side of the methodology. This chapter deals with the issues that are essential to construct a good model in practice. Such issues include the problem of input and experiment design. Typical essential features of the input are discussedUNESCO as well as examples of commonly – us edEOLSS inputs. Next comes the question of how to condition the measured signals. This involves issues of removing trends and disturbances outsideSAMPLE of the frequency range CHAPTERSs of interest for the model. The most demanding task is to find a suitable model structure, guided by information in the observed data. A first cut methodology for this is described. For a successful application, it is in the end a matter of combining intuition, and information from various data test.
    [Show full text]