Independent Graduate Modules– one 21 hours module per week (3 ECTS) Deadline for advance registration to each module: 31/12/2015 International Graduate School on Control www.eeci‐institute.eu/IGSC2016 (opening: 15/07/2015) Chair: Francoise Lamnabhi‐Lagarrigue <[email protected]> Registration will open on 15/07/2015 Different locations M01 – PARIS‐SACLAY 18/01/2016 ‐ 22/01/2016 Control by PDE modelling Enrique Zuazua, Universidad Autonoma Madrid, Spain M02 – PARIS‐SACLAY 25/01/2016 ‐ 29/01/2016 Control of biological systems Denis Dochain Université Catholique de Louvain, Belgium M04 – PARIS‐SACLAY 08/02/2016 ‐ 12/02/2016 Advanced topics in the optimal control of economic systems Raouf Boucekkine, Aix‐Marseille School of Economics, France M05 – PARIS‐SACLAY 15/02/2016 ‐ 19/02/2016 LMIs for optimization and control Didier Henrion & Jean‐Bernard Lasserre CNRS LAAS, University of Toulouse, France M06 – 2016 ‐ BOMBAY 15/02/2016 ‐ 19/02/2016 Introduction to Geometric Nonlinear Control Theory and Applications Witold Respondek, INSA Rouen, France M07 – BERLIN 22/02/2016 ‐ 26/02/2016 Modeling, analysis and design of wireless sensor and actuator networks Alessandro D'Innocenzo, University of L'Aquila & Carlo Fischione, KTH Royal Inst. Tech., Sweden M08 – BERLIN 29/02/2016 ‐ 04/03/2016 Control of discrete event systems Joerg Raisch, Technical University of Berlin, Germany & Laurent Hardouin, Université d’Angers, France M09 – PARIS‐SACLAY 29/02/2016 ‐ 04/03/2016 Randomized algorithms for systems, control and networks Roberto Tempo, CNR‐IEIIT, Politecnico di Torino, Italy M10 – PARIS‐SACLAY 07/03/2016 ‐ 11/03/2016 High‐gain observers in nonlinear feedback control Hassan K. Khalil, Michigan State University, USA M11 – PARIS‐SACLAY 14/03/2016 ‐ 18/03/2016 Stability, control, and computation for time‐delay systems Wim Michiels, K.U. Leuven, Belgium & Silviu‐Iulian Niculescu, CNRS, Paris‐Saclay, France M12 – BERLIN 14/03/2016 ‐ 18/03/2016 Model Predictive Control Jan Maciejowski, University of Cambridge, UK M13 – PARIS‐SACLAY 21/03/2016‐‐ 25/03/2016 Geometric mechanics and nonlinear control Ravi Banavar, IIT Bombay, Inde M14 – L’AQUILA 21/03/2016 ‐ 24/03/2016 Tools for nonlinear control, Lyapunov function, positivity, applications Frédéric Mazenc, INRIA, Paris‐Saclay, France M15 – L’AQUILA 04/04/2016 ‐ 08/04/2016 Cyber‐Physical systems control: Algebraic and Optimization techniques Raphaël Jungers, Université Catholique de Louvain, Belgium M16 – PARIS‐SACLAY 04/04/2016 – 08/04/2016 Distributed coordination of multi‐agent systems Wei Ren, University of California, Riverside, USA M17 – PARIS‐SACLAY 11/04/2016 – 15/04/2016 Nonlinear observers: applications to aerial robotic systems Robert Mahony, Jochen Trumpf, Australian Nat. Univ & Tarek Hamel, CNRS, Sophia‐Antipolis, France M18 – ISTANBUL 18/04/2016 – 22/04/2016 Stability and stabilization of time‐varying systems Elena Panteley & Antonio Loria CNRS, Paris‐Saclay, France M19 – ISTANBUL 25/04/2016 – 29/04/2016 Convergence theory for observers Laurent Praly, Mines‐ParisTech, France M20 – BELGRADE 25/04/2016 – 29/04/2016 Optimization and stabilization under large delays Miroslav Krstic, Univ California, San Diego, USA & Iasson Karafyllis, NTUA, Athens, Greece M21 ‐ ST PETERBURG 02/05/2016‐06/05/2016 Distributed control and computation A. Stephen Morse, Yale University, USA M22 – PARIS‐SACLAY 09/05/2016 – 13/05/2016 The interplay between Big Data and sparsity in control and systems identification Mario Sznaier, Northeastern Univ, MA, USA M23 – PARIS‐SACLAY 09/05/2016 – 13/05/2016 Time‐delay, sampled‐data and PDE systems Emilia Fridman, Tel Aviv University, Israel M24 – PARIS‐SACLAY 16/05/2016 – 20/05/2016 Geometric and numeric methods in optimal control with applications to engineering Bernard Bonnard & Jean‐Baptiste Caillau University of Burgundy, Dijon, France M25 – ISTANBUL 23/05/2016 – 27/05/2016 Nonlinear control techniques for modern engineering applications Romeo Ortega, CNRS L2S PARIS‐SACLAY, France M26 – PARIS‐SACLAY 23/05/2016 – 27/05/2016 Networked control with limited data rates Girish Nair, University of Melbourne, Australia M27 – PARIS‐SACLAY 31/05/2016 ‐ 03/06/2016 Practical adaptive control Anuradha Annaswamy, MIT, USA M28 – PARIS‐SACLAY 06/06/2016 ‐ 10/06/2016 Convex and set‐valued analysis for systems and control Rafal Goebel, Loyola University Chicago, USA M29 – ZURICH 06/06/2016 ‐ 10/06/2016 Nonlinear control for physical systems Roger W. Brockett, Harvard SEAS, USA & Alexandre L. Fradkov, RAS, St‐Petersburg, Russia
Transcript
Independent Graduate Modules– one 21 hours module per week (3 ECTS)
Deadline for advance registration to each module: 31/12/2015
International Graduate School on Controlwww.eeci‐institute.eu/IGSC2016 (opening: 15/07/2015)
Chair: Francoise Lamnabhi‐Lagarrigue <[email protected]>Registration will open on 15/07/2015
Different locations
M01 – PARIS‐SACLAY 18/01/2016 ‐ 22/01/2016
Control by PDE modelling Enrique Zuazua, Universidad Autonoma Madrid, Spain
M02 – PARIS‐SACLAY 25/01/2016 ‐ 29/01/2016
Control of biological systems Denis DochainUniversité Catholique de Louvain, Belgium
M04 – PARIS‐SACLAY 08/02/2016 ‐ 12/02/2016
Advanced topics in the optimal control of economic systems
Raouf Boucekkine,Aix‐Marseille School of Economics, France
M05 – PARIS‐SACLAY 15/02/2016 ‐ 19/02/2016
LMIs for optimization and control Didier Henrion & Jean‐Bernard Lasserre CNRS LAAS, University of Toulouse, France
M06 – 2016 ‐ BOMBAY 15/02/2016 ‐ 19/02/2016
Introduction to Geometric Nonlinear Control Theory and Applications
Witold Respondek, INSA Rouen, France
M07 – BERLIN 22/02/2016 ‐ 26/02/2016
Modeling, analysis and design of wireless sensor and actuator networks
Alessandro D'Innocenzo, University of L'Aquila &Carlo Fischione, KTH Royal Inst. Tech., Sweden
M08 – BERLIN 29/02/2016 ‐ 04/03/2016
Control of discrete event systems Joerg Raisch, Technical University of Berlin, Germany &Laurent Hardouin, Université d’Angers, France
M09 – PARIS‐SACLAY 29/02/2016 ‐ 04/03/2016
Randomized algorithms for systems, control and networks
Roberto Tempo, CNR‐IEIIT, Politecnico di Torino, Italy
M10 – PARIS‐SACLAY 07/03/2016 ‐ 11/03/2016
High‐gain observers in nonlinear feedback control
Hassan K. Khalil, Michigan State University, USA
M11 – PARIS‐SACLAY 14/03/2016 ‐ 18/03/2016
Stability, control, and computation for time‐delay systems
Model Predictive Control Jan Maciejowski, University of Cambridge, UK
M13 – PARIS‐SACLAY 21/03/2016‐ ‐ 25/03/2016
Geometric mechanics and nonlinear control Ravi Banavar, IIT Bombay, Inde
M14 – L’AQUILA 21/03/2016 ‐ 24/03/2016
Tools for nonlinear control, Lyapunov function, positivity, applications
Frédéric Mazenc, INRIA, Paris‐Saclay, France
M15 – L’AQUILA 04/04/2016 ‐ 08/04/2016
Cyber‐Physical systems control: Algebraic and Optimization techniques
Raphaël Jungers, Université Catholique de Louvain, Belgium
M16 – PARIS‐SACLAY 04/04/2016 – 08/04/2016
Distributed coordination of multi‐agent systems
Wei Ren, University of California, Riverside, USA
M17 – PARIS‐SACLAY 11/04/2016 – 15/04/2016
Nonlinear observers: applications to aerial robotic systems
Robert Mahony, Jochen Trumpf, Australian Nat. Univ & Tarek Hamel, CNRS, Sophia‐Antipolis, France
M18 – ISTANBUL 18/04/2016 – 22/04/2016
Stability and stabilization of time‐varying systems
Elena Panteley & Antonio Loria CNRS, Paris‐Saclay, France
M19 – ISTANBUL 25/04/2016 – 29/04/2016
Convergence theory for observers Laurent Praly, Mines‐ParisTech, France
M20 – BELGRADE 25/04/2016 – 29/04/2016
Optimization and stabilization under large delays
Miroslav Krstic, Univ California, San Diego, USA & Iasson Karafyllis, NTUA, Athens, Greece
M21 ‐ ST PETERBURG 02/05/2016‐06/05/2016
Distributed control and computation A. Stephen Morse, Yale University, USA
M22 – PARIS‐SACLAY 09/05/2016 – 13/05/2016
The interplay between Big Data and sparsity in control and systems identification
Mario Sznaier, Northeastern Univ, MA, USA
M23 – PARIS‐SACLAY 09/05/2016 – 13/05/2016
Time‐delay, sampled‐data and PDE systems Emilia Fridman, Tel Aviv University, Israel
M24 – PARIS‐SACLAY 16/05/2016 – 20/05/2016
Geometric and numeric methods in optimal control with applications to engineering
Bernard Bonnard & Jean‐Baptiste Caillau University of Burgundy, Dijon, France
M25 – ISTANBUL 23/05/2016 – 27/05/2016
Nonlinear control techniques for modern engineering applications
Romeo Ortega, CNRS L2S PARIS‐SACLAY, France
M26 – PARIS‐SACLAY 23/05/2016 – 27/05/2016
Networked control with limited data rates Girish Nair, University of Melbourne, Australia
M27 – PARIS‐SACLAY 31/05/2016 ‐ 03/06/2016
Practical adaptive control Anuradha Annaswamy, MIT, USA
M28 – PARIS‐SACLAY 06/06/2016 ‐ 10/06/2016
Convex and set‐valued analysis for systems and control
Rafal Goebel, Loyola University Chicago, USA
M29 – ZURICH 06/06/2016 ‐ 10/06/2016
Nonlinear control for physical systems Roger W. Brockett, Harvard SEAS, USA & Alexandre L. Fradkov, RAS, St‐Petersburg, Russia
M01 – PARIS‐SACLAY18/01/2016 ‐ 22/01/2016
Control by Partial Differential Equation modelling
Outline
1.‐ Historical introduction2.‐ Introduction to finite‐dimensional control3.‐Wave propagation4.‐ Heat diffusion5.‐ Some relevant models of multi‐physics nature.6.‐ Numerical approximation of control problems7.‐ Averaged control on parameter depending systems8.‐ Switching, sparse and bang‐bang control9.‐ The turnpike property10.‐ Pespectives and open problems
References• J. M. Coron, Control and Nonlinearity, AMS, 2009.• S Ervedoza, E. Z. On the numerical approximation of exact controls for waves, SpringerBriefs in Math., 2013, XVII.• E. Trélat. Contrôle optimal: théorie& applications. Vuibert. Collection "Mathématiques Concrètes", 2005.• E Trélat, E. Zuazua. Turnpike property in finite‐dimensional nonlinear optimal control, JDE, 218 (2015), 81‐114.• E. Zuazua, Controllability and Observability of Partial Differential Equations: Some results and open problems, in Handbook of
Differential Equations: Evolutionary Equations, vol. 3, C. M. Dafermos and E. Feireisl eds., Elsevier Science, 2006, pp. 527‐621.• E. Zuazua, Switching control, J. Eur. Math. Soc., 2011, 13, 85‐117.• E. Zuazua, Averaged controllability, Automatica, 50 (2014) 3077–3087.
Summary of the course
In this series of lectures we shall discuss several topics related with the modelling, analysis, numericalsimulation and control of Partial Differential Equations (PDE) arising in various contexts of Science andTechnology. In these lectures we shall introduce some of the most relevant work that has been done in thesubject in recent years, paying special attention to the fundamental methodological aspects, and pointingtowards some potential future perspectives of research.
We shall first describe and document some of the most relevant applications to Sciences, Engineering andTechnology in which these problems arise from an historical viewpoint. After a short introduction to thefinite‐dimensional theory, we shall then describe the basic theory for the wave and heat equation, to lateraddress some important multi‐physics models. Then we shall address the problem of the numericalapproximation of control problems. To begin with we shall show that the control and the numericalapproximation process do not commute so that, in general, when controlling a finite‐dimensionalapproximation of the continuous model, one does not actually compute an approximation of thecontrol one is looking for. We shall see what are the possible remedies to these pathologies: spacediscretizations, numerical damping, filtering of high frequencies, multi‐grid algorithms, etc.. The latter factis of great impact from a modelling point view since in practical applications numerical approximationschemes may also be used (and they are often used that way) as discrete models. We shall also presentsome interesting concepts and results on switching, sparse, averaged and bang‐bang control, and theturnpike property ensuring that, most often, in long‐tie horizons, optimal controls and trajectories are closeto the steady‐state ones. To conclude, we shall present a list of open problems and directions of possiblefuture research.
Enrique ZuazuaBCAM & IKERBASQUE
Basque Foundation for Science, Bilbao, Spain http://www.ikerbasque.net/enrique.zuazua
Aim : The objective of this course is to give an introduction and cover recent aspects of dynamicalmodeling, monitoring and control of biological systems. The course will cover the following topics :
Dynamical modeling of biological systems : the notion of reaction networks and mass balancemodeling will be introduced as a central concept to build a general dynamical model for biologicalsystems. It will be used to model the biological system at the level of the cell (via the notions ofmetabolic engineering) up to the interaction mechanisms among different species (by consideringmicrobial ecology notions). The model will cover both homogeneous conditions, known as stirredconditions in reactors for instance (described by ODE’s (ordinary differential equations)) and nonhomogeneous ones, encountered e.g. in incompletely mixed reactors, such as plug flow and diffusionbased conditions in reactors, as well as population balance models that describe the distribution of ageor mass of the cells (described by PDE’s (partial differential equations)). Mathematical concepts of thegeneral dynamical model, including reaction invariant, model reduction and stability, as well asmicrobial ecology concepts like the competitive exclusion principle, will be studied. The link withmetabolic engineering will also be introduced. The course will also cover the identification of bioprocessmodels (including the structural and practical model identifiability and the design of optimalexperiments for parameter estimation). It will also address simulation issues related to PDE models andthe use of reduction methods for this type of models.
Several practical applications will be used to illustrate the techniques and principles covered in thiscourse. Examples will include biological systems from the food industry and the pharmaceutical industryto the environment and the (waste) water treatment. Computer hands‐out exercices will be integratedin the course.
M02 – PARIS‐SACLAY25/01/2016 ‐ 29/01/2016
Control of biological systems: from the cell to the environment
Denis DochainICTEAM,
Université catholique de Louvain, Belgiumhttp://www.uclouvain.be/denis.dochain
Monitoring : this part of the course will bededicated to the design applications of stateobservers (Luenberger observers, Kalman filters,asymptotic observers, finite‐time convergingobservers, …) and parameter estimation algorithms(in particular to estimate reaction rates and yieldcoefficients), that take advantage of the specificstructural properties of the biological systemmodels.
Control : the course will emphasize optimal controland (adaptive) linearizing control (includingadaptive extremum seeking). The choice of thesecontrol approaches will be motivated in the contextof biosystem applications.
Abstract of the course
This course reviews some selected advanced topics in the optimal control of economic and demo‐economic systems. Three main topics will be studied. The first focus will be on age‐structured models ineconomy and demography and the associated infinite‐ dimensional optimization problems. Adaptedmethods based on calculus of variations and dynamic programming will be presented and applied to aseries of economic and demo‐economic problems. The second topic concerns the optimal control ofspatio‐temporal systems typically governed by parabolic partial differential equations with an applicationto optimal economic growth. Finally, some recent optimal regime switching problems will be treated withapplications to ecological economics.
M04 – PARIS‐SACLAY08/02/2016 ‐ 12/02/2016
Advanced topics in the optimal control of economic systems
LMIs, linear matrix inequalities, have been studied extensively since the 1990s in connection withLyapunov techniques for ensuring stability and performance of linear and nonlinear control systems.This approach to systems control constantly benefits from developments and improvements ofefficient interior‐point primal‐dual algorithms for conic optimization by the mathematicalprogramming community.
Recent achievements of real algebraic geometry have provided powerful results for the representationof positive polynomials as sum‐of‐squares (SOS) and its dual theory of moment problems. Manydifficult nonlinear nonconvex optimization and control problems can now be solved numerically andefficiently by moment‐SOS LMI hierarchies, with mathematically sound convergence guarantees andexplicit certificates of global optimality. Our public‐domain Matlab package GloptiPoly, developedsince 2002, implements many of these techniques and ideas.
The main purpose of this course is to introduce the basic concepts of this general methodology anddetail its application for solving nonlinear nonconvex optimal control problems with polynomial data.
M06 – 2016 ‐ BOMBAY15/02/2016 ‐ 19/02/2016
Introduction to Geometric Nonlinear Control Theory and Applications
Witold RespondekNormandie Universite, INSA de Rouen, France
The aim of the mini‐course is two‐folds. In the first part we will introduce basic notions, tools, and resultsof geometric control theory. We will discuss the concepts of controllability, observability, decoupling, andequivalence in the context of nonlinear control systems. We will recall and/or introduce geometric toolson which the theory is based (Lie brackets, distributions and co‐distributions, integral manifolds, Frobeniustheorem etc.). In the second part, we will present more recent results concerning equivalence of controlsystems under state‐space equivalence, feedback equivalence, and dynamic equivalence. In particular, wewill discuss feedback linearization, equivalence of control‐linear systems to the chained forms (and theirapplications to nonholonomic systems), flatness, and describe control systems that admit a mechanicalstructure. Throughout the mini‐course we will emphasize the geometric character of the nonlinear controltheory and its applications to various control synthesis problems (stabilization, tracking, nonlinearobservers). We will illustrate the course by physical, mainly mechanical, examples
1. Geometric tools of nonlinear control (Lie bracket, distributions, Frobenius theorem).2. Nonlinear controllability (Lie rank, orbit theorem, Chow‐Rashevsky theorem, accessibility).3. Nonlinear observability (Krener‐Hermann theorem, observable/nonobservable decomposition)4. State‐space, feedback and dynamic equivalence of control systems. State‐space and feedback
linearization.5. Controlled invariant distributions, nonlinear decoupling, and zero dynamics6. Nonholonomic systems and control‐linear systems equivalent to the chained forms7. Flatness and at control systems.8. Mechanical control systems.
Outline:
Alessandro D’InnocenzoDepartment of Information Engineering,Computer Science and Mathematics
Center of Excellence DEWS, University of L’Aquila, Italyhttp://people.disim.univaq.it/~alessadin/
Modeling, analysis and designof wireless sensor and actuator networks
Abstract of the course:The massive deployment of smart and wirelessly interconnected devices in cyber physical systems isproviding extensive information from the physical world through distributed sensing mechanisms. With theemergence of low‐cost controllers/actuators that can be potentially embedded in everything (e.g., vehicles,robots, buildings, human body), the sensed information can be utilized to act and perform control, estimationand monitoring at an unprecedented scale. This is demanding the development of Wireless Sensor Networkand Actuators Networks (WSAN) fundamental design principles so to reliably and certifiably observe thephysical world, processing the data, making decisions based on the sensor observations and performingappropriate control actions. This course is devoted to the study of such systems.WSAN may require low latency, reliable communications and controls, and even energy efficient operationswhen energy is a scarce resource. This is challenging because reliability and latency are at odds, and resourceconstrained nodes may support only simple algorithms. In this course, a system‐level design approach for co‐design of Control Systems and Protocols supporting control applications over WSAN is given: in particular, wewill discuss the following scenarios:Control‐aware network design, when the protocol parameters can be adapted by an optimization problemwhose objective function is a network or control utility, and the constraints are the reliability and latency ofthe messages as requested by a control application: these algorithms allow the network to meet thereliability and latency required by the control application while taking into account network and control costs;Network‐aware controller design, when the controller can be adapted to guarantee some controlspecifications robustly with respect to networking non‐idealities;Joint optimization (or co‐design) of controller, networking layer, medium access control layer and physicallayer;Cross‐layer adaptation and optimization, where desirable signaling between communication layers enablesimultaneous computation of control actions and networking configuration to improve the overall systemperformance.
Topics: • Wireless channel and protocol layers modeling over WSAN• Mathematical modeling of closed‐loop systems over WSAN• Robust, resilient and secure control co‐design over WSAN• Distributed estimation and optimization over WSAN• Discussion of open problems and opportunities for research
Abstract :In many areas of application, properties that are interesting from a control point of view are naturallycharacterised via (timed or untimed) sequences of discrete events. This is true for many manufacturingand transportation systems, but also holds for processes from other application domains on certainlevels of abstraction. The dynamic behaviour of such processes is described by Discrete Event Systems(DES). This course will provide an introduction to DES and does not require any background knowledgeon this subject. We will address modelling, analysis and (optimal) control aspects. The course will coverlanguage and behavioural models, characterising DES by sets of finite or infinite strings of discreteevents, and their realisations in terms of Petri net and finite automaton, or state machine, models. It willdiscuss the basic ideas of Supervisory Control Theory, aiming at providing minimally restrictive controlfor problems where both the plant and the specification can be modelled by finite automata. Theoptimal (just‐in‐time) feedforward control and feedback control for a subclass of Timed Petri nets thatdescribe synchronisation phenomena will be presented. Finally, we will address the question whetherfinite state abstractions can be used to design control for infinite state systems.
Topics:
1. Introduction2. Petri Nets
2.1. Petri Net Graphs 2.2. Petri Net Dynamics 2.3. Special Classes of Petri Nets 2.4. Analysis of Petri Nets 2.5. Control of Petri Nets 2.6. Timed Petri Nets
3. Dioid Algebras3.1. Timed Event Graphs (TEGs) with Holding Times 3.2. The Max‐Plus Algebra and Residuation Theory 3.3. State Equations for TEGs in the Max‐Plus Algebra 3.4. Optimal Control (Just‐in‐Time Control) 3.5. Closed Loop Control and State Estimation
4. Supervisory Control Theory4.1. Languages and Automata 4.2. Maximally Permissive Control 4.3. Control Implementation by Finite Automata
5. Abstraction Based Control
M08 – BERLIN29/02/2016 ‐ 04/03/2016
Control of discrete event systems
M09 – PARIS‐SACLAY29/02/2016‐04/03/2016
Randomized algorithms forsystems, control and networks
Roberto TempoCNR‐IEIIT, Politecnico di Torino, Italyhttp://staff.polito.it/roberto.tempo/
AbstractIn this course, we provide a perspective of the research area of randomization for systems, control andnetworks. In particular, we study several topics which are of interest when dealing with control of uncertainsystems and networks described by graphs.
Randomization is a key tool to handle uncertain systems and control problems which can be solved onlyapproximately due to partial or contaminated data, or because only local information about the network isavailable. Various techniques are developed in the course to construct synchronous and asynchronoussequential algorithms for analysis and design. Convergence and optimality properties of these algorithmsare analyzed.
We also discuss several applications, which include stochastic model predictive control, anti‐windupcompensation, the PageRank computation, control design of unmanned aerial vehicles and clocksynchronization of wireless networks. The course is based on the book by R. Tempo, G. Calafiore, F.Dabbene, “Randomized Algorithms for Analysis and Control of Uncertain Systems, with Applications,” 2nd
edition, Springer, London, 2013.
Topics: ‐ Uncertain systems, networks and graphs‐Monte Carlo and Las Vegas algorithms‐ Random sampling techniques‐ Probabilistic methods for control design‐ Distributed randomized algorithms‐ Systems and control applications
Abstract of the course
High‐gain observers play an important role in the design of feedback control for nonlinear systems. This courseteaches the essentials of high‐gain observers, their use in various control problems, including stabilization,tracking and regulation, and the challenges encountered in implementing them. The target audience areengineers from multiple disciplines (electrical, mechanical, aerospace, chemical, etc.) and appliedmathematicians. Prerequisite: graduate‐level knowledge of nonlinear systems analysis, especially Lyapunovstability.
The course is designed around the upcoming research monograph:H.K. Khalil, High‐Gain Observers in Nonlinear Feedback Control (expected in 2017)
Outline
1. Introduction and observer design2. Stabilization and tracking3. Adaptive control4. Regulation5. Extended observer6. Unmodeled dynamics and measurement noise7. Sampled‐data control
The aim of this course is to describe fundamental properties of systems subjected to time‐delays and topresent an overview of methods and techniques for the analysis and control design. The focus lies onsystems described by functional differential equations and on frequency domain techniques, grounded innumerical linear algebra (e.g., eigenvalue computations) and optimization, but the main principles behindtime‐domain methods are addressed as well. Several examples (from chemical to mechanical engineering,from haptics systems and tele‐operation to communication networks, from biological systems topopulation dynamics and genetic regulatory networks) complete the presentation. The course iscomplemented with home‐works where control design problems are solved using recently developedsoftware.
Wim MichielsDepartment of Computer Science
KU Leuven, Belgiumhttp://people.cs.kuleuven.be/wim.michiels
Stability, Control, and Computation for Time‐delay Systems
Abstract of the courseModel Predictive Control (MPC) is a model‐based method which uses online optimization in real timeto determine control signals. It is the only practical control method that takes account of systemconstraints explicitly, and the only ‘advanced control’ method to have been adopted widely in industry,particularly in petrochemicals and other process industries. There is intense interest in it for a varietyof other applications, including automotive, aerospace, electric drives, smart grid and paper‐making.This course covers the theory from basics through to current research concerns, as well as practicalaspects. It includes paper‐and‐pencil andMatlab‐based exercises. The course has been given in variousuniversities since 2001, and has recently been comprehensively revised and updated.
Jan M. MaciejowskiCambridge University, Department of Engineering, UK
• Various formulations of MPC• Solution methods for MPC• Stability and recursive feasibility• Tuning MPC and reverse engineering• Robust MPC• Explicit MPC• Nonlinear MPC• ‘Economic’ MPC• Case studies and applications
The course is based on the textbookPredictive Control with Constraints, by J.M. Maciejowski, Prentice‐Hall, 2002.
This course will present the modeling and control ofmechanical systems in a geometric setting. Theapplication domain would be mechanical andaerospace engineering, in particular, the applicationsof attitude stabilization of a quadrotor and rolling/wheeled mobile robots wouldbe presented.
Main references:
‐ Geometric Control of Mechanical Systems ‐ F. Bullo and A. D. Lewis, Springer, 2005.‐ Geometric Mechanics and Symmetry ‐ D .D. Holm, T. Schmah and C. Stoica, Oxford University Press, 2009.‐ Nonholonomic Mechanics and Control ‐ A. M. Bloch, Springer, 2003‐ A Mathematical Introduction to Robot Manipulation and Control ‐ R. Murray, Z. Li and S. Sastry, CRC Press, 1992‐ Introduction to Mechanics and Symmetry ‐ J. Marsden and T. Ratiu, Springer‐Verlag, 1994.
Motivational examples: Satellite/quadrotor attitude stabilization, control of wheeled/spherical mobilerobots.
Smooth manifolds machinery: An introduction to differentiable manifolds, tangent vectors, vectorfields, co‐vector fields, immersions and submersions, vector fields, integral curves, push‐forward andpull‐back of vector fields. Lie groups, actions of groups, Lie algebras, adjoint co‐adjoint maps,symmetries.
Riemannian manifolds: The metric tensor, covariant derivative, the connection and geodesic motion,the Euler‐Lagrange equations on a Riemannian manifold
Regulation problems on Riemannian manifolds: configuration error functions, stabilization, region ofattraction.
Tracking problems on Riemannian manifolds: the transport map and compatibility conditions.
Outline :
1) Introduction to dynamical systems: Ordinary DifferentialEquations, discrete‐time systems, time‐varying systems, basicnotions (existence and uniqueness of solutions, finite escapetime phenomenon). Notions of stability (local, global, basin ofattraction), notion of input‐to‐state stability.
2) Fundamental results. Linear systems: stability analysis,linearization. Hartman‐Grobman Theorem, Two dimentionalsystems : Poincaré–Bendixson theorem. Dulac’s criterion,properties of ω‐limit sets.
3) Lyapunov functions: Lyapunov theorem, converse Lyapunovtheorem, LaSalle Invariance Principle. Weak Lyapunovfunctions, strict Lyapunov functions, Matrosov Theorem.Construction of strict Lyapunov functions. Determination of anestimate of a basin of attraction via a strict Lyapunov functions.Notion of ISS Lyapunov function.
4) Control design: Lyapunov design, Jurdjevic‐Quinn theorem,classical backstepping, bounded backstepping, backstepping fortime‐varying systems, strabilization and tracking thoughforwarding, Sontag‘s formula.
5) Positive systems: Cooperative nonlinear systems, linear positivesystems, linear Lyapunov function. Notion of interval observer.
M14 – L’AQUILA21/03/2016 ‐ 24/03/2016
Tools for nonlinear control, Lyapunov function, positivity, applications
Frederic MazencLaboratoire des Signaux et Systèmes (L2S)CNRS‐CentraleSupélec‐U PSUD, France
We will present fundamental results pertaining to ordinarydifferential equations, discrete‐time systems and nonlinearcontrol theory. In particular, we will review the notion ofLyapunov function, the LaSalle Invariance Principle, theJurdjevic‐Quinn’s theorem and the techniques calledbackstepping and forwarding. We will perform constructionof strict Lyapunov functions. We will study the notion ofpositive systems. We will study several applied problems(chemostats, PVTOL, cart‐pendulum system).
The module is partially based on the research monograph:M. Malisoff, F. Mazenc, Constructions of Strict LyapunovFunctions, Spinger‐Verlag, serie : Communications andControl Engineering, 2009
Models Switching systems hybrid automata Markov Decision Processes Graphs and Networks in control
Techniques: LMI's, Sum‐of‐Squares, s‐procedure,Tarski's procedure, sub‐gradient methods,Automata theoretic techniques for hybrid systems
Abstract of the course
While autonomous agents that perform solo missions can yield significant benefits, greater efficiency andoperational capability will be realized from teams of autonomous agents operating in a coordinatedfashion. Potential applications for networked multiple autonomous agents include environmentalmonitoring, search and rescue, space‐based interferometers, hazardous material handling, and combat,surveillance, and reconnaissance systems. Networked multi‐agent systems place high demands onfeatures such as low cost, high adaptivity and scalability, increased flexibility, great robustness, and easymaintenance. To meet these demands, the current trend is to design distributed coordination algorithmsthat rely on only local interaction to achieve global group behavior. The objective of this course is tointroduce some recent results in the field of distributed coordination of multi‐agent systems. Topicscovered include consensus seeking, motion coordination, distributed average tracking, and distributedestimation as well as their applications in multi‐vehicle cooperative control (e.g., ground robots, UAVs,spacecraft, robotic arms, sensor networks).
M16 – PARIS‐SACLAY04/04/2016 – 08/04/2016
Distributed coordination of multi‐agent systems
Outline
1. Overview of recent research in multi‐agentcoordination and control
2. Distributed consensus in multi‐agent systems (fundamental continuous‐ and discrete‐time local averaging algorithms, consensus for agents with linear or nonlinear dynamics, applications)
Nonlinear observers: applications to aerial robotic systems
Abstract of the course
The functionality of any robotic system depends critically on its ability to estimate its dynamic state. Foraerial robotic systems, with limited sensor suites, highly dynamic motion, non‐linear state space, andlimited computational capacity, the state observer performance is even more important. A keytechnology enabler underlying the explosion of small scale commercial aerial robotic systems seen inthe last five years was the development of high quality, simple, robust, attitude observers. This courseprovides an introduction to the theory underlying design of observers for kinematic systems withsymmetry that was fundamental in this development. The approach taken is based on matrix calculusand Lie theoretic foundations, and students will be given an introduction to these topics from anengineering perspective. The course is based around an extensive suite of case studies drawn from aerialrobotic applications including; attitude estimation, velocity aided attitude estimation, pose estimation,and homography estimation. Students will come out of the course with a strong understanding of howto derive and implement nonlinear observers for real world robotic systems.
Topics: 1) Perspectives on observer design for physical systems.2) Matrix calculus and matrix ODEs.3) Lyapunov observer design for systems with matrix state.4) Dealing with practical issues, velocity bias, asynchronous measurements and delays.5) Lie theory foundations, Kinematic systems with symmetry.6) Second‐order‐optimal minimum‐energy filters
Practical work in this course uses MATLAB (or equivalent scripting language) extensively. Students arerequired to have a working system on their own laptop for the course. The real‐time implementationexercise will be undertaken in C++ in a virtual machine that will be provided. A SIMULINK environmentwill be available for students without C++ programming experience for this component of the course.
Stability and Stabilisation of Time‐varying systems[Lyapunov stability without Lyapunov functions]
Abstract of the course
This course focusses on the nonlinear control problems related to physical systems such as robots, marinevehicles, motors, etc. Realistic scenarios impose uncertainties in the parameters and the impossibility ofmeasuring the whole system's state. Solving such problems through systematic Lyapunov‐based design mayrapidly become intractable only because of our inability to construct strict Lyapunov functions.
We study a number of analysis methods (alternative to Lyapunov’s) which allow to establish strongproperties of stability and robustness in scenarios of tracking control problems, dynamic output‐feedback,observer‐based separation principle for physical systems. These methods generalise well‐known results forautonomous systems, such as Lasalle’s invariance principle, to the case of time‐varying systems.
Topics:
Areas:
‐ Integrability conditions (Refinements of Barbalat);‐ Differential methods reminiscent of Lasalle’s invariance principle (Matrosov);‐ Adaptive control and closed‐loo identification;‐ Dynamic output‐feedback and invariance principle;‐ Linear time‐varying systems and consensus;
‐ Robot tracking control;‐ Sensorless control of electrical motors;‐ Formation control of autonomous vehicles;‐ Nonholonomic systems;‐ Synchronisation.
M19 – ISTANBUL25/04/2016 – 29/04/2016
Convergence theory for observers
Abstract of the course
Context:Observers are objects delivering estimation of variables which cannot be directly measured. Theaccess to such "hidden" variables is made possible by combining modeling and measurements. Butthis is bringing face to face real world and its abstraction with as a result the need for dealing withuncertainties. The corresponding theoretical observers are consequently very complex, multivaluedand often extremely difficult to implement. This implies that approximations and simplifications areinvolved with, as a consequence, convergence problems.
Content:As introduction we state the observation problem in its full generality and mentionn possibletheoretical answers. This shows that an observer is nothing but a dynamical system withmeasurements as inputs and estimates as outputs. We restrict ourselves with the case where thissystem is finite dimensional and when there is no uncertainty. We concentrate our attention on theconvergence aspect with first giving necessary condition and then sufficient conditions. Particularemphasis is given to general purpose observers as high gains observers and nonlinear Luenbergerobservers.
Model‐free optimization (also known as Extremum Seeking, ES) and model‐based stabilization have much incommon. While ES deals with unknown setpoints for stable plants, and stabilization deals withknown/desired setpoints for unstable plants, both problems employ feedback for setpoint convergence.The recent confluence of ES and stabilization allows a beginner to get into both subjects with greater easethan previously possible. In addition, advances in delay compensation allow both optimization andstabilization to be solved under arbitrarily large delays on inputs and measurements.
Our course will cover both ES and predictor‐based control of nonlinear systems with delays. The coursestarts with a review of the most important ES techniques for static and dynamic systems, usingdeterministic and stochastic perturbations, emulating gradient‐ and Newton‐based optimization, andaddressing both single‐agent optimization and non‐cooperative multi‐agent games. The course’s secondhalf covers control of nonlinear systems under delays on inputs and outputs, with implementations overnetworks with delay uncertainty and using sampled‐data, and using approximations of predictor mappings.(This is the only EECI course this year covering general nonlinear networked‐based designs under arbitrarilylarge and uncertain delays.) The course concludes with an application of the predictor tools to ESalgorithms under large input or measurement delays.
No knowledge of time‐delay systems is required and all concepts are explained by means of numerousexamples and illustrated by applications in energy systems (renewable and combustion based), robotics,aerospace, biology, economics, manufacturing, and chemical engineering.
Outline: ‐ Review of ES techniques for single agent optimization problems‐ ES for non‐cooperative multi‐agent games‐ Predictor Feedback for Delay Systems‐ Predictor Feedback under partial measurement
M21 ‐ ST PETERBURG 02/05/2016‐06/05/2016
Distributed control and computation
Abstract of the courseOver the past decade there has been growing in interestin distributed control problems of all types. Amongthese are consensus problems including flocking anddistributed averaging, the multiagent rendezvousproblem, and the distributed control of multi‐agentformations. The aim of these lectures is to explain whatthese problems are and to discuss their solutions.Related concepts from spectral graph theory, rigid graphtheory, nonhomogeneous Markov chain theory, stabilitytheory, and linear system theory will be covered. Amongthe topics discussed are the following.
Flocking: We will present graph‐theoretic results appropriate to the analysis of a variety of consensusproblems cast in dynamically changing environments. The concepts of rooted, strongly rooted, andneighbor ‐shared graphs will be defined, and conditions will be derived for compositions of sequencesof directed graphs to be of these types. As an illustration of the use of the concepts covered, graphtheoretic conditions will be derived which address the convergence question for the widely studiedflocking problem in which there are measurement delays, asynchronous events, or a group leader.
Distributed Averaging: By the distributed averaging problem is meant the problem of computing theaverage value of a set of numbers possessed by the agents in a distributed network using onlycommunication between neighboring agents. We will discuss a variety of double linear iterations anddeadlock‐free, deterministic gossiping protocols for doing distributed averaging.
Formation Control: We will review recent results concerned with the maintenance of formations ofmobile autonomous agents {eg robots} based on the idea of a rigid framework. We will talk brieflyabout certain classes of “directed” rigid formations for which there is a moderately completemethodology. We will describe recently devised potential function based gradient laws forasymptotically stabilizing “undirected” rigid formations and we will illustrate and explain what happenswhen neighboring agents using such gradient laws have slightly different understandings of what thedesired distance between them is suppose to be.
Topics will include:1. Flocking and consensus2. Distributed averaging via broadcasting3. Gossiping and double linear iterations4. Multi‐agent rendezvous5. Control of formations6. Convergence rates7. Asynchronous behavior8. Consensus‐based approach to solving a linear equation9. Stochastic matrices, graph composition, rigid graphsperformance recovery via
A. Stephen MorseDepartment of Electrical Engineering
The Interplay Between Big Data and Sparsity inControl and Systems Identification
These efforts have resulted in new approaches, that draw from many disparate areas, ranging from semi‐algebraic geometry to sparse signal recovery and matrix completion, and exploit the underlying structure ofthe problem to obtain tractable relaxations (and is some cases exact solutions) to computationally hardproblems. The goal of this short course is twofold: (1) provide a quick introduction to the subject forpeople in the systems community faced with “big data” and scaling problems, and (2) serve as a “quickreference” guide for researchers, summarizing the state of the art as of today and provide acomprehensive set of references. Part I of the course covers the issue of handling large data sets andsparsity priors in systems identification and model (in)validation, presenting very recently developedtechniques that exploit a deep connection to semi‐algebraic geometry, rank minimization and matrixcompletion. Part II of the course continues this theme, but focusing on control and filter design. The courseconcludes by illustrating these ideas using examples from several application domains, including machinelearning, computer vision, systems biology and economics.
Mario SznaierDepartment of Electrical and Computer Engineering
AbstractArguably, one of the hardest challenges faced nowby the systems community stems from theexponential explosion in the availability of data,fueled by recent advances in sensing technology.Simply stated, classical techniques are ill equippedto handle very large volumes of (heterogeneous)data, due to poor scaling properties and to imposethe structural constraints required to implementubiquitous sensing and control. To overcome theseshortcomings, during the past few years a largeresearch effort has been devoted to developingcomputationally tractable methods that seek tomitigate the “curse of dimensionality” byexploiting the twin blessings of self‐similarity (highdegree of spatio‐temporal correlation in the data)and concentration of measure (inherentunderlying sparsity).
Course outline1. Mathematical Foundations: ‐ Review of convex optimization and Linear Matrix Inequalities – Review of
semi‐algebraic geometry – Promoting sparsity via optimization. Convex surrogates for cardinality andrank – Fast algorithms for convex optimization – Polynomial optimization: Sum‐of‐squares andmoments based approaches – Exploiting sparsity in polynomial optimization.
2. Sparsity in Systems Identification: – Identification of LTI systems with missing data and outliers –Identification of sparse graphical models – Identification of Wiener systems – Semi‐supervisedidentification of switched affine systems – Model invalidation.
3. Sparsity in Control and Estimation: – Synthesis of controllers subject to sparsity constraints: the convexcase – Synthesis of controllers subject to sparsity flow constraints: the general case – Sparse filterdesign for LTI systems – Worst case optimal filters for switched systems.
4. Connections to Machine Learning: – Robust regression and subspace clustering – Manifold embeddingas a Wiener identification problem.
5. Applications: – Actionnable information extraction as a SysId problem – Finding causal interactions as asparse graphical model identification – Recovering 3D geometry from 2D data as aWiener identificationproblem – Anomaly detection as a model (in)validation problem – Multitarget tracking as a rank‐minimizing assignment problem.
Abstract
Time‐delay appears naturally in many control systems. It isfrequently a source of instability although, in some systems, itmay have a stabilizing effect. A time‐delay approach to sampled‐data control, which models the closed‐loop system as continuous‐time with delayed input/output, has become popular innetworked control systems (where the plant and the controllerexchange data via communication network). The beginning of the21st century can be characterized as the "time‐delay boom"leading to numerous important results. The emphasis of thecourse is on the Lyapunov‐based analysis and design for time‐delay, sampled‐data and networked control systems. An LMIapproach to some classes of PDEs will be discussed.
The course is designed around the text book:E. Fridman, Introduction to Time‐Delay Systems: Analysis andControl. Birkhauser, 2014.
M23 – PARIS‐SACLAY 09/05/2016 – 13/05/2016
Time‐delay, sampled‐data and PDE systems
http://www.springer.com/gp/book/9783319093925
Outline
1. Models of systems with time‐delay: sampled‐data and networked‐control systems, traffic flow and drillingpipe models.
2. Basic theory. Classification of time‐delay systems, existence of solutions. Solution of linear non‐homogenous equations. Controllability, observability of linear systems.
3. Stability and performance analysis. Direct Lyapunovapproach: Krasovskii and Razumikhim methods. An LMI approach to stability and performance. The small gain theorem approach.
4. Control design: predictor‐based control, LQR problem. LMI approach to robust stabilization and H1 control. Systems with saturated actuators.
5. Discrete‐time delay systems.6. Sampled‐data and networked control systems: a time‐
delay approach.7. PDEs: an LMI approach to analysis and design.
Emilia FridmanSchool of Electrical Engineering,
Tel Aviv University, Israelhttp://www.eng.tau.ac.il/ emilia/
Optimal control is key to addressing problems, e.g. in classical or quantum mechanics. In thiscourse, we review the basics of optimal control with an emphasis on the geometricalviewpoint. On the algorithmic side, cutting edge methods will be presented during hands‐on courses on real‐world applications.
Outline
Theoretical background.1. Lie algebraic methods for controllability2. First and second order optimality conditions in control3. Averaging in optimal control
Hands on.4. Spacecraft trajectory optimization (hampath)5. Energy management (l1‐magic)6. Medical imaging by NMR (BOCOP, GloptiPoly)
The topics covered in the course include the following:
1. Modeling and control of multi‐machine power systems: transient stability problems.
2. Modeling and control of large scale hydraulic networks.3. Modeling and control of microgrids: analysis of droop controllers.4. Adaptive and nonlinear control of mechanical systems: pendular systems,
teleoperators and flexible structures.5. Adaptive and nonlinear control of power converters: continuous and discontinuous
conduction modes.6. Adaptive and nonlinear control electromechanical systems: sensorless control of
motors, solar and wind generating units, wind speed estimation.7. Nonlinear control of electrical systems: power factor compensation in
non{sinusoidal regimes, effect of constant power loads.8. Dynamic energy routers.9. The theoretical tools used to address the previous problems include the following.10. Port‐Hamiltonian and Euler‐Lagrange models.11. Passivity‐based control.12. Nonlinear PI control.13. Immersion and invariance observers and adaptive controllers.
M25 – ISTANBUL23/05/2016 – 27/05/2016
Nonlinear control techniques for modern engineering applications
Abstract
Goal of this course is to present a class of recentlydeveloped tools for the modeling, analysis and controlof several modern engineering applications. Unlikeother control courses, the material is always motivatedby a specific practical application and presentedside{by{side with the existing approach. In this way, thestudent is able to confront the advantages (if any) ofadopting the new perspective vis{a{vis the classicalviewpoint that prevails in the specific application.Romeo Ortega
Laboratoire des Signaux et Systèmes (L2S)CNRS‐CentraleSupélec‐U PSUD, France
In modern control systems, components suchas sensors, controllers and actuators are oftenconnected to one another by digital channelsof finite communication capacity. At their limitsof performance, such systems exhibitimportant properties that can be understoodonly by examining their control andcommunication aspects jointly.
This course introduces some of the mainconcepts and theoretical results governing theanalysis and design of networked controlsystems with limited data rates, based ontechniques from control, quantisation theory,information theory and dynamical systems. Nobackground knowledge is assumed, apart frombasic control theory.
Topics will include:
1. Stochastic linear systems controlled via a digital channel – minimal data rates and universalperformance bounds via information theory; construction and analysis of stabilising policies thatapproach minimum rate
2. Nonlinear systems controlled via a digital channel‐ topological feedback entropy; minimal datarates for set invariance
3. Distributed linear systems connected by a digital network ‐ network information theory; when isinformation a fluid flow; conditions for system stability
4. An introduction to nonstochastic information and directed nonstochastic information for worst‐case estimation and control.
Abstract
Adaptive Control is viewed as a game changer in many application domains where real‐time feedbackcontrol is essential to ensure the desired performance. Adaptive controllers, whose distinguishingfeature is a parameter estimator that prescribes the rule for changing the control parameters in real‐time, have been studied extensively over the past forty years, with fundamental properties of stabilityand robustness well understood. Guidelines for analysis and synthesis for adaptive controllers have beenlaid out for linear and (specific classes of) nonlinear systems, continuous and discrete‐time systems,single‐input and multi‐input systems, and deterministic and stochastic systems.
So what’s missing?
There are glaring gaps in adaptive control theory that remain to be closed for adaptive control to be aviable, practical, and easily implementable methodology. Guarantees have to be provided that ensurerobustness to a wide variety of non‐parametric perturbations. Guidelines have to be in place for asystematic design of all free parameters in the controller. Bounds have to be derived for not only steady‐state behavior but also for transient characteristics. Implementation issues will have to be satisfactorilyaddressed. The ability to accommodate actuator constraints in terms of bandwidth, magnitude limits,and rate limits has to be precisely characterized.
Recently, there have been breakthroughs in Adaptive Control that have led to reducing the above gaps.This course will provide not only the foundation of the classical adaptive control theory, but alsohighlight these recent results and show how they contribute towards making adaptive control practical.
M26 – PARIS‐SACLAY23/05/2016 – 27/05/2016
Practical adaptive control
Topics
Adaptive control theory – first‐order plant,states accessible, output feedback
Adaptive control with closed‐loop referencemodels and solutions to transients
Robust Adaptive Control
Examples and case studies from aerospace andautomotive systems
Anuradha AnnaswamyActive‐adaptive Control Laboratory
Problems in Dynamics and Control where Convex and Set‐Valued Analysis is Useful
Abstract
The course is a tutorial on set‐valued and convex analysis, motivated by and with applications to problemsinvolving dynamics and control.
Classical control problems largely rely on linear dynamics, linear feedback, and quadratic Lyapunovfunctions. Nonlinear systems may require nonlinear, discontinuous, or hybrid feedback, while saturation,switching, state constraints, impacts, etc. introduce further variety of behaviors. Considered systems maydisplay irregular dependence of solutions on initial conditions, sensitivity to perturbations, lack ofquadratic Lyapunov functions, piecewise structure, discontinuous evolution, etc. Set‐valued analysis,convex analysis, as well as nonsmooth analysis, have helped researchers deal with similar issues inoptimization and optimal control for many years. This course presents selected material from set‐valuedand convex analysis oriented toward analysis of problems in control theory beyond optimal control.Background in nonlinear systems is expected from the audience and some experience with mathematicalanalysis may be helpful.
M28 – PARIS‐SACLAY 06/06/2016 ‐ 10/06/2016
Convex and set‐valued analysis for systems and control
Rafal GoebelDepartment of Mathematics and Statistics
Loyola University Chicagohttp://webpages.math.luc.edu/~rgoebel1/
Set‐valued mappings and their regularity, and what theyhave to do with robustness of feedback control systems orhow they can be used to model complex hybrid dynamics.
Tangent and normal cones to sets, and what they say aboutweak and strong invariance of sets or about optimalsolutions to constrained optimization problems, and howthey can be used in ``linearization''.
Convergence of sets and how decreasing sets appear in theanalysis of consensus algorithms.
Properties of convex functions, and how parametricoptimization involving such functions leads to explicitsolutions of the famous constrained LQR problem.
Convex Lyapunov functions and their convex conjugates,and how they arise in stability analysis of linear switchingsystems and their duals.
Abstract of the courseTechnological developments have led to a new, exciting and powerful synthesis of physics and control,building on the classical work of notable physicists such as Huygens, Carnot, Szilard, and Kapitza Examplesas diverse as managing electric power grids and optimizing inputs for magnet resonance spectroscopy areamong topics of current interest. Of course, most of these interesting problems fall well outside the usuallinear, quadratic, Gaussian framework. In this course, the unifying principles coming from theconsideration of energy, momentum, and reduction principles will be extended to include control terms.Emphasis will be placed on the role of geometrical ideas such as metrics, symplectic structures, Poissonand Lie brackets, etc., when they serve to best explain matters. Examples will be drawn from cyber‐physical systems of current interest and the type of control mechanisms that have proven to be effective inthis setting.
Topics will include:Control of conservative systems; Control of dissipative systems; Synchronization, Chaos and Convergence;Statistical Mechanics and Learning Theory, Quantum control and Quantum information,
