European Embedded Control Institute › EECI-docs2 › EECI-Modules-2011.pdf · An Introduction to Netw – M10 21/03/2011 – 25/03/2011 Specification, Desig Distributed Emb M11

European Embedd

EECIEECI--HYCON2 HYCON2 GraduGraduwww.eeci-instit

Sprin

15 INDEPENDENT MODULES – one

Lectures taug

Deadline for ADVANCE REGISTRA

Location: Supelec

M117/01/2011 ‐ 21/01/2011 Flatness and Nonlinear

M224/01/2011 28/01/2011 Controlled Synchronisati

Location: Supelec

24/01/2011 ‐ 28/01/2011 y

M331/01/2011 – 04/02/2011 The Behavioral Approach

M407/02/2011 – 11/02/2011 LMI, Optimization and

M514/02/2011 – 18/02/2011 Optimization on

M6 Cooperative NavigationM621/02/2011 – 25/02/2011

Cooperative NavigationRobotic

M728/02/2011 ‐ 04/03/2011 Normal Forms for Non

M807/03/2011 – 11/03/2011

High‐Gain Observers Con

M914/03/2011 18/03/2011 An Introduction to Netw14/03/2011 – 18/03/2011

M1021/03/2011 – 25/03/2011

Specification, DesigDistributed Emb

M1128/03/2011 – 01/04/2011 Modeling and analysis

M1204/04/2011 ‐ 08/04/2011 Control of Highly

M13M1326/04/2011 ‐ 29/04/2011 Model Predi

M1402/05/2011 – 06/05/2011 Robust Hybrid C

M1509/05/2011 – 13/05/2011

Optimality, Stabilizain Nonline

ded Control Institute

uateuate SchoolSchool on Controlon Controltute.eu/GSC2011

ng 2011

e 21 hours module per week (3 ECTS)

ght in English

ATION to each module: 21/12/2010

c (South of Paris)

r Estimation Techniques Michel Fliess

ion of Dynamical Systems Antonio Lorỉa / El P t l

c (South of Paris)

f y y Elena Panteley

h to Modeling and Control Harry L. Trentelman /Paolo Rapisarda

d Polynomial Methods Didier Henrion

Matrix Manifolds Rodolphe Sepulchre /Pierre Antoine Absil

n and Control of Multiple Antonio M Pascoal /n and Control of Multiple Vehicles

Antonio M. Pascoal / Antonio P. Aguiar

nlinear Control Systems Witold Respondek

in Nonlinear Feedback ntrol Hassan Khalil

worked Control Systems Karl Henrik Johansson / Vijay GuptaVijay Gupta

n and Verification of bedded Systems

Richard Murray /Ufuk Topcu

s of biological networks Mustafa Khammash

Nonlinear Systems Claude Samson /Pascal Morin

ictive Control Eduardo F. Camacho

Control Systems Ricardo G. Sanfelice

ation, and Feedback ear Control Francis Clarke

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M117/01/2011 ‐ 21/01/2011

Abstract of

Fl t liFlat non‐linbeginning omodel‐basedimensionasystems, whhere by revyan algebrairesp. diffesystems. Thconcept ofclearcut maand of fauand of fauwhich solvetheory, areof noisy signonlinear abe investiga

Michel FliessLaboratoire LIX

Ecole Polytechnique, Francehttp://www.lix.polytechnique.fr/~fliess/


Flatness and Nonlinear Estimation Techniques

the course:

t hi h i t d d t thnear systems, which were introduced at theof the 90s, provide a most efficient tool for theed control of many concrete finite‐al case‐studies. This approach to nonlinearhich is now quite popular in industry, is taughtvisiting the classic concept of controllability viag p yic setting which introduces modules over rings,erential fields, for linear, resp. nonlinear,he same algebraic tools allow to revisit theobservability and therefore to define also in aanner the notions of parameter identifiabilityult diagnosis The corresponding estimatorsult diagnosis. The corresponding estimators,e many pending questions in nonlinear systemderived from a powerful numerical derivation

gnals, which will be analyzed and compared toasymptotic observers. Numerous examples willated during the lectures.

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M2 CM224/01/2011 ‐ 28/01/2011

Co

Antonio LoriaL2S, CNRS – Supelec – Université Paris Sud 11

Francehttp://www.lss.supelec.fr/perso/loria/

Abstract of the course: Synchronisation isystems behave in a coordinated way. Cinduce or to destroy synchronisation via ansynchronization is a broad domain of renumber of disciplines such as (mathematicnumber of disciplines such as (mathematicelectromechanical, electronic), applied maTwo broad paradigms are open: analysis awhy and how synchronisation happens naphenomenon that appears in flocks of birdin perfectly coordinated groups; the motirespect to both its neighbour's and the grodevelopment (analysis and design) is targastonishing applications such as a cure forabout controlling how synchronisationapplication field is Telecommunicationsinformation to a receiver. Roughly, the scinformation to a receiver. Roughly, the sctransmitter which generates a chaotic sinformation. A receiver is controlled to mrecover the encrypted information i.e.,Hence, if the receiver circuit is “tunned” totransmitter, the data may be recovered byi l C t ll d h i ti hsignal. Controlled synchronisation has enorformation: ongoing ship replenishment,consensus: clusters of satellites ...


ll d S h i i f D i lontrolled Synchronisation of Dynamical Systems

Elena PanteleyL2S, CNRS – Supelec – Université Paris Sud 11

Francehttp://www.lss.supelec.fr/perso/panteley/

s the property by which several dynamicalControlled synchronisation is the ability ton external force i.e., a control input. Study ofesearch and development which covers acal) physics biology engineering (electricalcal) physics, biology, engineering (electrical,thematics, mechatronics, to mention a few.and design. Analysis is about understandingaturally. In Biology e.g., synchronisation is as and schools of fish which migrate or travelion of each individual is synchronised withoup itself. In Medicine, recent research andgeted towards models of neuron cells withr brain diseases such as Parkinson. Design isis willed to happen. An important R&Ds: consider a transmitter which sendscenario consists in implementing a chaoticcenario consists in implementing a chaoticsignal that serves as carrier for valuablemimic the behaviour of the transmitter toit must synchronise with the transmitter.generate the same chaotic carrier as the

y extracting the carrier from the transmittedi t i th h hi lrmous impact in other aereas such as vehicle

teleoperation and more generally, agents

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M331/01/2011 – 04/02/2011

Paolo RapisardaUniv. of Southampton, UK

http://users.ecs.soton.ac.uk/pr3/

Abstract of the course: The aim of thiscontrol from the behavioral point of visystems.

The behavior of a dynamical system is the sby the laws governing the system. To obtaiwe view a complex system as the interconnsubsystems and their interconnection. Thisthe variables of interest, also auxiliary varcomprising higher‐order differential equatithe variables In the behavioral setting conthe variables. In the behavioral setting, cona controller; thus we accommodate also tview of the controller as a signal processocontrol of mechanical systems. Stabilizatiformulated concisely and effectively in thwhich dissipates the energy supplied to itlinear systems, quadratic functionals of tmeasure the rate of energy supply and theand quadratic differential forms providefunctionals. Optimal‐ and H∞‐ control probcalculus.

The course will deal with the topics outlinedaimed at familiarizing the attendees with th


Modeling, analysis and control of dissipative system behaviors

Harry L. TrentelmanUniv. of Groningen, NL

http://www.math.rug.nl/ trentelman/

course is introduce modeling, analysis andew, with special emphasis on dissipative

set consisting of all time‐trajectories allowedin a mathematical description of a behavior,nection of subsystems, and we describe theprocedure yields a model involving, besidesriables describing the interconnections, andons, often with algebraic constraints amongntrol is viewed as interconnecting a plant tontrol is viewed as interconnecting a plant tohose situations in which the usual point ofor is not applicable, for example in passiveion and pole placement problems can behis framework. A dissipative system is onefrom the external world. When consideringthe system variables and their derivativese rate of dissipation. The calculus of bilinears an effective way of representing theseblems can be formulated elegantly using this

d on this page, and include exercise sessionshe material illustrated during the lectures.

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M407/02/2011 – 11/02/2011 LMI,

Abstract ofstudents ofalgebra, conlinear contrprogramminoptimizationmoments andynamical sy

The first pmathematicmathematicsurvey. Weduality. Werepresentedof liftingsemialgebrah h dhow these idsolutionsproblems,inequalitiesproblem ofof‐squares d

Didier HenrionLAAS‐CNRS, Univ. Toulouse,

France &Fac. Elec. Engr., Czech Tech. Univ in Prague, Czech Rep. o squa es d

semialgebraalgorithmic a

The secondcontrol appl i l t

http://homepages.laas.fr/henrion

classical staconnectionmainstreamand secondnotion of odefined on pp


Optimization and Polynomial Methods

the course: This is a course for graduatef researchers with a background in linearnvex optimization and some knowledge inrol systems. The focus in on semidefiniteng (SDP), or linear matrix inequality (LMI)n, and its interplay with the problem ofnd semialgebraic geometry in the context ofystems control.

part of the course describes fundamentalal features of LMIs startingwith a historicalal features of LMIs, startingwith a historicalreview the notions of convexity, cones andclassify convex semialgebraic sets that can bed with LMIs, and we introduce the key notionvariables allowing to represent convexic sets as projections of LMIs. Then we showd b l d ddeas can be exploited to provide constructiveto nonconvex polynomial optimizationincluding bilinear or polynomial matrix(PMIs), using a formulation as a primal

moments and a dual problem of finding sum‐decomposition of polynomials nonnegative ondeco pos o o po y o a s o ega e oic sets. We also survey numerical andaspects and latest software developments.

part of the course focuses on systems andplications of these techniques, first in at li f k l i i thate‐space linear framework, explaining thewith standard Lyapunov techniques androbust control techniques from the 1990s,in a polynomial framework, insisting on the

occupation measures for dynamical systemspolynomial vector fields.p y

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M514/02/2011 – 18/02/2011 Op

Abstract of the course: The recent years h

Rodolphe SepulchreDept. Electrical Engineering & Computer Science

Université de Liège, Belgiumhttp://www.montefiore.ulg.ac.be/~sepulch/

ydevelopment of efficient optimization algorparticular embedded and quotient matrix mlinear algebra (eigenproblems), statisticComponent analysis), large‐scale optimizatsignal processing (blind source separati(clustering regression on nonlinear spaces)(clustering, regression on nonlinear spaces)a few. Good algorithms result from thegeometry, optimization and numerical analytutorial introduction to this rich field ofselection of topics in differential geometillustration of engineering problems wherewill provide the participants with theinstrumental to algorithmic development.provides a natural foundation for the develmany equality‐constrained optimization ptechniques, such as steepest descent, contype methods are generalized to the manifotype methods, are generalized to the manifothese methods is provided, building upon tthen guided through the constructions andformulated methods into concrete numericaare illustrated on several problems in lineoptimization, computer vision, and statisticto specific applications. Matlab sessions wiby‐step implementation of illustrative algorthe freely downloadable monograph "Opt(Princeton University Press, 2008).


ptimization on Matrix Manifolds

have witnessed an increasing interest in the

ePierre Antoine Absil

Dept.Mathematical EngineeringUniversité catholique de Louvain, Belgique

http://www.inma.ucl.ac.be/~absil/

grithms defined on special nonlinear spaces, inmanifolds. Applications abound in numericalcal analysis (Principal and Independention (sparse and rank‐constrained problems),on, subspace tracking), machine learningcomputer vision (pose estimation) to name, computer vision (pose estimation), to name

e combination of insights from differentialysis. The purpose of the course is to provide aapplied mathematics with a parsimonious

try and in numerical algebra, and with ane the theory is currently applied. The coursebasic concepts of differential geometryIt will illustrate why differential geometry

lopment of efficient numerical algorithms forproblems. Several well‐known optimizationnjugate gradients, trust‐region and Newton‐old setting A generic development of each ofold setting. A generic development of each ofthe geometric material. The participants ared computations that turn these geometricallyal algorithms. The techniques are general andear algebra, signal processing, data mining,cal analysis. Specific lectures will be devotedll allow the students to experience the step‐rithms. The course material will be based ontimization Algorithms on Matrix Manifolds"

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M621/02/2011 – 25/02/2011

Coop

Antonio M. PascoalDynamical Systems and Ocean Robotics LabInstitut for Systems and Robotics, Portugal

http://welcome.isr.ist.utl.pt/people/index.asp?accao=showpeople&id people=35

Abstract of the course: This course focusemultiple autonomous vehicles. It is organizescenarios: description of scientific mission

p p p _p p

autonomous vehicles. 2) Theoretical Foundrelated to vehicle modeling in the presevehicle navigation and control, cooperativcontrol in general in the face of stringenIssues: how to go from theory to practice;vehiclesvehicles.

Outline:1. Introduction: An historical perspective; Pr2. Autonomous Vehicles Models: Hovercraunderwater vehicle; Unmanned aerial vehic3. Nonlinear Control theory (a brief review)Lyapunov based analysis and design tools4. Dynamic positioning of autonomous vehpresence of external disturbances5. Trajectory‐tracking and path‐following ofTrajectory‐tracking controller design; PathTrajectory tracking controller design; Pathparametric uncertainty; Performance limitat


perative Navigation and Control of Multiple Robotic Vehicles

Antonio P. AguiarDynamical Systems and Ocean Robotics LabInstitut for Systems and Robotics, Portugal

http://users.isr.ist.utl.pt/~pedro/

es on the theme of cooperative control ofed around the following themes: 1) Missionscenarios that require the use of multipleations: covering a whole spectrum of issuesnce of environmental disturbances, singleve navigation and control, and networkednt communication constraints. 3) Practicallessons learned from experiments with real

ractical motivation and mission scenariosft; Autonomous surface craft; Autonomouscle): Lyapunov Stability; Input to state stability;

hicles: Point‐stabilization; Positioning in the

f autonomous vehicles: Problem statement;h‐following controller design; Dealing withh following controller design; Dealing withtions

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Abstract of the course: The aim of this c

M728/02/2011 ‐ 04/03/2011 Norm

normal forms for various classes of nonlinobtained during the last 30 years for vatracking, motion planning, observation esystematic way, by providing normal formequivalence to them, and (whenever theythem We will show usefulness of the prthem. We will show usefulness of the prproblems: linearization, flatness, stabilizanonlinear observers.

Outline:1 F db k1. Feedback2. Feedback3. Globally fe4. Partial fee5. Special cla5a. System5b. Locally

6. Triangular6a. Lower6b. p‐norm6c. Upper6d LinearWitold Respondek

Département Génie MathématiquesMont‐Saint‐Aignan, Rouen, Francehttp://lmi.insa‐rouen.fr/~wresp/

6d. Linear7. Formal fee7a. Gener7b. Feedfo

8. Normal fo8a. Chaine8b. Locally

9. Normal fo10. Nonlinea10a. Local10b. Glob


course is to present a fairly complete list of

al Forms for Nonlinear Control Systems

p y pnear control systems. Such forms have beenarious purposes: classification, stabilization,etc. We will attempt to present them in ams, necessary and sufficient conditions fory exist) algorithmic procedures for obtainingresented forms in various nonlinear controlresented forms in various nonlinear controlation, output and trajectory tracking, and

d t t i land state equivalence.linearizable systems.eedback linearizable systems.edback linearization.asses of control systems.ms on R2y simple systems.r forms.triangular forms and feedback linearizability.mal forms.triangular forms and feedforward systems.

rizable feedforward systemsrizable feedforward systemsedback and formal normal forms.al systems.orward systems.orms for driftless systemsed formsy simple driftless systemsorms for observed dynamics.ar control systems with observations.l normal forms.al normal forms

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M807/03/2011 – 11/03/2011 High‐Ga

Hassan KhalilDept. Electrical & Computer Engineering

Michigan State University , USA http://www egrmsu edu/~khalil/

Abstract of t

The theory ofor about tw

http://www.egr.msu.edu/ khalil/

for about twtheory withrole of contnonlinear seuse of high‐gcontrol proregulation,performancesampled‐datand nonlineaExtended Kaextended higextended hig


ain Observers in Nonlinear Feedback Control

he course:

of high‐gain observers has been developedwenty years In this module we introduce thewenty years. In this module, we introduce theemphasis on the peaking phenomenon, thetrol saturation in dealing with it, and theparation principle. We present results on thegain observers in various nonlinear feedbackoblems, including stabilization, tracking,and adaptive control. We examine

e in the presence of measurement noise,a control, and observers with time‐varyingar gains. We show a connection with thealman Filter and present recent results ongh‐gain observers.gh gain observers.

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M914/03/2011 – 18/03/2011 An Int

Karl Henrik JohanssonACCESS Linnaeus Centre

School of Electrical EngineeringKTH, Stockholm, Sweden

Abstract of the course:

Networked control systems have emerged a

KTH, Stockholm, Swedenhttp://www.s3.kth.se/~kallej/

components of a dynamical system havcommunication capabilities. Analysis and dtools from various information sciencesdistributed processing, and so on. This setthe theory and tools for building such system

Topics:1. Markov jump linear systems2. Estimation and control in the presence of3. Effects of quantization4. Information patterns5 Di t ib t d ti ti d f i5. Distributed estimation and sensor fusion6. Consensus and distributed control7. Event based control8. Applications in cooperative control


troduction to Networked Control Systems

Vijay GuptaDepartment of Electrical Engineering

University of Notre Dame, USAhttp://ee.nd.edu/faculty/vgupta/

as a major research area in recent years as

http://ee.nd.edu/faculty/vgupta/

ve been equipped with processing andesign of such systems requires a fusion ofs, such as information theory, control,of lectures will provide an introduction toms.

delay and packet loss

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M1021/03/2011 – 25/03/2011

Specific

Richard MurrayCalifornia Institute of Technology, USA

http://www.cds.caltech.edu/~murray/wiki/Main_Page


Increases in fast and inexpensive computinggeneration of information‐rich control systemexecution distributed optimization sensor fexecution, distributed optimization, sensor fsophisticated ways. This course will providmethods and tools for specifying, designisystems. We combine methods from cochecking, synthesis of control protocols) wcontrol (Lyapunov functions, sum‐of‐squares

l d d i i ll hanalyze and design partially asynchronous coaddition to introducing the mathematical teand prove properties, we also describe aanalyzing and synthesizing hybrid control srobust performance specifications. The follow

* Transition systems and hybrid I/O auto* Specification of behavior using linear t* Algebraic certificates for continuous an* Approximation of continuous systems * Verification of (asynchronous) control * R di h i t l l i l* Receding horizon temporal logic plann


cation, Design and Verification of Distributed Embedded Systems

Ufuk TopcuCalifornia Institute of Technology, USAhttp://www.cds.caltech.edu/~utopcu/

index.html

and communications have enabled a newms that rely on multi‐threaded networkedfusion and protocol stacks in increasinglyfusion and protocol stacks in increasinglyde working knowledge of a collection ofng and verifying distributed embeddedomputer science (temporal logic, modelwith those from dynamical systems ands certificates, receding horizon control) to

l l f iontrol protocols for continuous systems. Inchniques required to formulate problemsa software toolbox that is designed forsystems using linear temporal logic andwing topics will be covered in the course:

omataemporal logicnd hybrid systemsusing discrete abstractionsprotocols using model checkingiing

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Abstract of

M1128/03/2011 – 01/04/2011 Mod

throughoutsystems useinternal michanges in twill developfor exploringfor exploringthese toolsbiological coat the sysrobustness aengineering

Mustafa KhammashUniversity of California at Santa Barbara, USA

of the unbiological sythe ever‐pre

http://www.engineering.ucsb.edu/~khammash/

A key source of this noise is the randomnconstituents at the molecular level. Cfluctuations (over time) within individualvariability among clonal cellular populatiunderstand that the richness of stochasupon the interactions of dynamics and nothese interactions occur. We review astochastic fluctuation in gene expression.stochastic fluctuation in gene expression.methods for the analysis of stochastictechniques using examples of gene regulat

Tentative syllabus:• Introduction to gene expression andD t i i ti t h ti d l• Deterministic vs. stochastic models.

• Mass‐action kinetics. Michaelis‐Men• Deterministic modeling at the system• Feedback and feedforward strategie• Biological oscillations.• The stochastic chemical kinetics fram• A rigorous derivation of the chemica• Linear vs. nonlinear propensities.


the course: Regulation is a running theme

deling and analysis of biological networks

biology. At every level of organization, livinge feedback control strategies to regulate theirlieu in order to withstand the constanttheir external environment. In this course wep the modeling and analysis tools necessaryg regulatory mechanisms in biology We useg regulatory mechanisms in biology. We uses to study some examples of intricateontrol mechanisms at the molecular level andstem level, showing how they achieveand performance and drawing analogies withcontrol systems. We will also highlight some

nique operating conditions under whichystems achieve their function. Among these isesent noise at the cellular level.

ness that characterizes the motion of cellularCellular noise not only results in randoml cells, but it is also a source of phenotypicons. Researchers are just now beginning totic phenomena in biology depends directlyise and upon the mechanisms through whichnumber of approaches for the analysis ofWe will explore analytical and computationalWe will explore analytical and computationality in living cells, and demonstrate thesetory networks that suppress or exploit noise.

d gene regulatory networks.

nton kinetics. Reaction rate equations.m and cellular levels.es.

mework.al master equation. Moment computations.

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M1204/04/2011 ‐ 08/04/2011

Claude SamsonINRIA, France

http://www.inria.fr/personnel/Claude Samson fr html


The course in an introduction to the Transv

Claude.Samson.fr.html

by P. Morin and C. Samson to control nonlinequilibria but whose linear approximation isto as "critical" systems, and the fact thatexplains in part the difficulty posed by theirstabilizers in the form of continuous pure‐sta Brockett's theorem for a large subclass oa Brockett s theorem for a large subclass o"universal" feedbacks capable of stasymptotically, as proved in a work bydevelopment of control solutions that depaThe practical stabilization of non‐feasible trin the control literature, constitutes ah i l i i itheoretical aspects, an important motivatiothe fact that many physical systems can bcase, for instance, of nonholonomic mechawheels, ranging from common car‐like vehand of many underactuated vehicles (likeAsynchronous electrical motors also belongy g


Control of Highly Nonlinear Systems

Pascal MorinINRIA, France

erse Function approach recently developednear systems that are locally controllable ats not. Such systems are sometimes referredt they are not state‐feedback linearizabler control. The non‐existence of asymptoticaltate feedback controllers, as pointed out byf critical systems, and the non‐existence off critical systems, and the non existence ofabilizing all feasible state‐trajectoriesy Lizzaraga, are also incentives for theart from "classical" nonlinear control theory.rajectories, a preoccupation little addressedcomplementary incentive. Beyond thesef h l i l i fon for the control engineer also arises from

be modeled as critical systems. Such is thenical systems (like most mobile vehicles onhicles to ondulatory wheeled‐snake robots)e ships, submarines, hovercrafts, blimps).to this category.g y

European Embedd

M1326/04/2011 ‐ 29/04/2011

Abstract

M d lModelconsideraacademiaPredictiveposing thability toyAlthoughacademicthe last tstabilitymature dand attraand attra

This courtheoreticcontrollestrategies

Eduardo F. CamachoDpto. Ingeniería de Sistemas y Automática

Escuela Superior de Ingenieros, Sevilla, Spainhttp://www.esi2.us.es/

propertieTopics sustabilitytracking,dealt with

~eduardo/home_i.html


Model Predictive Control

of the course:

P di ti C t l (MPC) h d l dPredictive Control (MPC) has developedably in the last decades both in industry and ina. This success is due to the fact that Modele Control is perhaps the most general way ofhe control problem in the time domain and itshandle constraints and multivariable processes.p

h the technique originated in industry, thec research community has contributed, duringtwo decades, important results, specially in thedomain. Although MPC is considered to be adiscipline, the field has still many open problemscts the attention of many researcherscts the attention of many researchers.

rses provides an extensive review concerning thecal and practical aspects of predictivers. It describes the most commonly used MPCs, especially, showing both the theoreticales and their practical implementation issues.uch as multivariable MPC, constraints handling,and robustness properties, fast realizations,multi‐objective, hybrid and stochastic MPC areh in the course.

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M1402/05/2011 – 06/05/2011

Abstract of

Hybrid contsystems withat involvethat involveand in genevents —themselvesallowing fosystems wcomputers,demand forwhich arethat mayperformancthe presen

Ricardo G. SanfeliceDept. Aerospace the presen

present rechybrid conproperties.modeling fmodern m

t ti

& Mechanical EngineeringUniversity of Arizona, USA

http://www.u.arizona.edu/~sricardo/

asymptoticsystematicprinciples.stabilizationdisplayed imanipulatopsystems.


Robust Hybrid Control Systems

the course:

trol systems arise when controlling nonlinearith hybrid control algorithms — algorithmse logic variables timers computer programe logic variables, timers, computer program,neral, states experiencing jumps at certainand also when controlling systems that ares hybrid. Recent technological advancesor and utilizing the interplay between digitalwith the analog world (e.g., embeddedsensor networks, etc.) have increased the

r a theory applicable to the resulting systems,of hybrid nature, and for design techniquesy guarantee, through hybrid control,ce, safety, and recovery specifications even ince of uncertainty. In the workshop, we willce of uncertainty. In the workshop, we willcent advances in the theory and design ofntrol systems, with focus on robustnessIn this course, we will present a general

framework for hybrid systems and relevantathematical tools. Next, we will introducet bilit d it b t d d ibstability and its robustness, and describe

tools like Lyapunov functions and invarianceThe power of hybrid control for (robust)n of general nonlinear systems will bein applications including control of roboticors, autonomous vehicles, and juggling, , j gg g

European Embedd

M1509/05/2011 – 13/05/2011

O

Abstract of

This coursenonlinear cand disconbe motivatissues in othroughoutequations,intended fo

Francis ClarkeInstitut Camille Jordan

Université Claude Bernard Lyon 1http://math.univ‐lyon1.fr/~clarke/ intended fo

Topics inclu1. Dyvariati2. Somwe ne3. Lya4. Dis5. Slid


Optimality, Stabilization, and Feedback in Nonlinear Control

the course:

e presents some modern tools for treating trulycontrol problems, including nonsmooth calculustinuous feedback. The need for such tools willted, and applications will be made to centraloptimal and stabilizing control. The contextt is that of systems of ordinary differentialand the level will be that of a graduate courseor a general control audience.or a general control audience.

ude:ynamic optimization: from the calculus ofions to the Pontryagin Maximum Principleme constructs of nonsmooth analysis, and whyd thed thempunov functions, classical to moderncontinuous feedback for stabilizationding modes and hybrid systems

European Embedded Control Institute › EECI-docs2 › EECI-Modules-2011.pdf · An Introduction to Netw – M10 21/03/2011 – 25/03/2011 Specification, Desig Distributed Emb M11

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