Graduate school in Systems, Optimization, Control and Networks (SOCN)

 
 

Graduate school courses scheduled in the academic year

2008-2009

 

Fall 2008


"CONTROL AND NONLINEARITY"
Lecturer : Jean-Michel CORON (Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions, France)

 

"INTRODUCTION TO DERIVATIVE-FREE OPTIMIZATION "
Lecturer : Luis N. VICENTE (University of Coimbra, Portugal)

 

"OPTIMAL CONTROL AND OPTIMIZATION"

Lecturer : Erik VERRIEST (Georgia Institute of Technology)

 

 

Spring 2009

 

"SOME TOPICS IN COMBINATORIAL OPTIMIZATION"
Lecturers : Satanu DEY and Marco DI SUMMA (UCL, Belgium)

 

"SUBSPACE BASED IDENTIFICATION IN FREQUENCY DOMAIN AND MODELLING WITH ORTHONORMAL BASES FUNCTIONS "
Lecturer : Huseyin AKCAY (Anadolu University, Turkey)

 

"LINEAR AND NONLINEAR OBSERVERS WITH APPLICATIONS TO FAULT DETECTION AND ISOLATION"
Lecturers : Michel KINNAERT (ULB, Belgium) and Gildas BESANCON (INP Grenoble, France)

 

 

 

Detailed contents

 

 

1. CONTROL AND NONLINEARITY

 

Lecturer : Jean-Michel CORON (Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions, France)

 

Aim of the course

 

The aim of this course is to present methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various explicit methods are presented to study the controllability and to construct stabilizing feedback laws. The power of these methods is illustrated by examples coming from such areas as robotics, celestial mechanics, fluid mechanics, and quantum mechanics.

 

Contents

 

I. Control of linear systems
I.1. Finite-dimensional linear control systems (Gramian of controllability, Kalman's type conditions)
I.2. Linear partial differential equations (duality, moments theory, multiplier method, Carleman inequalities)
II. Control of nonlinear systems
I.1 Controllability of nonlinear systems in finite dimension (linear test, iterated Lie brackets, return method)
I.2 Controllability of nonlinear systems in infinite dimension (linear test, iterated Lie brackets, return method, power series expansion, quasi-static deformations)
III Stabilization
III.1 Finite dimensional control systems : general results (pole-shifting theorem and applications, obstructions to feedback stabilization, time-varying feedback laws)
III.2 Feedback design tools (with applications to finite dimensional control systems and nonlinear partial differential equations)

 

Prerequisites

 

Basic knowledge in analysis (differential calculus, Hilbert spaces, ordinary differential equations) . No specific background in control theory or partial differential equations will be assumed.

 

Supporting material

 

The course will be primarily based on the book : Control and nonlinearity, Jean-Michel Coron, Mathematical survey and monographs, volume 136, 2007, American mathematical Society.

The preface of this book is available at http://www.ams.org/bookstore/pspdf/surv-136-pref.pdf

The table of contents of this book is available at http://www.ams.org/bookstore/pspdf/surv-136-toc.pdf

 

Dates : October 06, 07, 13, 14, 20, 21, 2008.

 

Schedule :

October 6, 13, 20 -> 14h00-17h00

October 7, 14, 21 -> 09h15-12h15

 

This course will take place at CESAME, Bâtiment Euler, 4, av. G. Lemaître, 1348 Louvain-la-Neuve

 

Paper 1

 


2. INTRODUCTION TO DERIVATIVE-FREE OPTIMIZATION

 

Lecturer : Luis N. Vicente (University of Coimbra, Portugal)

 

 

Contents

 

The first part of the course is dedicated to Sampling and Modeling. We will first cover positive spanning sets and bases, linear interpolation and regression models, and simplex gradients. Then we consider nonlinear polynomial interpolation models, in a determined, regression and underdetermined form, respectively, covering issues like well poisedness, Lagrange polynomials, conditioning, minimum norm Frobenius models, and Taylor-type error bounds. We will finish this part with constructive ways to ensure that well poisedness holds and some material on derivative-free models.

 

The second part of the course is on Frameworks and Algorithms. We will address: (i) direct-search methods where sampling is guided by desirable sets of directions (including global convergence with integer lattices and sufficient decrease); (ii) direct-search methods based on simplices and operations over simplices, of which a classical example is the Nelder-Mead method (for which we present a globally convergent variant); (iii) line-search methods based on simplex derivatives, establishing a connection with the implicit-filtering method; (iv) trust-region based methods, including the relationship with derivative-based methods, the abstraction to fully-linear and fully-quadratic models, a comprehensive global convergence analysis, and more practical aspects of trust-region interpolation-based methods.

 

The third part of the course concerns some relevant topics like surrogate models built by techniques different from polynomial interpolation or regression and rigorous optimization frameworks to handle surrogates. A survey of constrained derivative-free optimization is also presented as well as some extensions to other classes of problems, in particular global optimization. We will also review the existent software for derivative-free optimization.

 

Supporting material

 

The course is based on the upcoming book: Introduction to Derivative-Free Optimization, A. R. Conn, K. Scheinberg,

and L. N. Vicente, MPS-SIAM Series on Optimization, SIAM, Philadelphia, to appear in 2008/2009.

 

Dates : November 24, 26, 28 and December 01, 03, 05, 2008

 

Schedule : Attention !!!! 9:45-12:30

 

Room 00.62

 

This course will take place at the Katholieke Universiteit Leuven,
Department Elektrotechniek ESAT, Kasteelpark Arenberg 10, 3001 Heverlee

 

 

For the course see :

http://www.mat.uc.pt/~lnv/dfo-course

 

 

 

3. OPTIMAL CONTROL AND OPTIMIZATION

 

Lecturer : Erik VERRIEST (Georgia Institute of Technology)

 

 

Contents


Lecture 1. Parameter Optimization Problems
1.1 Unconstrained Optimization: Gradient and Newton Algorithms
1.2 Problems with Equality Constraints: Lagrange Multipliers
1.3 Problems with Inequality Constraints: Kuhn-Tucker method
1.4 Minimal Sensitivity Design


Lecture 2. Discrete Optimal Control - Calculus of Variations
2.1 Single Stage Systems
2.2 Discrete Optimal Control Problems
2.3 Maximum Accuracy Control
2.4 Calculus of Variations, Lagrangian Dynamics


Lecture 3. Function Optimization (Cont'd)
3.1 Controllability
3.2 Fixed Interval, Optimal Control with Final State Constraints
3.3 Free Final Time Problems: General Bolza Problem
3.4 Periodic Optimal Control


Lecture 4. Dynamic Optimization Problems with Path Constraints
4.1 Integral Constraints
4.2 Control Equality Constraints
4.3 Control Inequality Constraints, Pontryagin Maximum Principle,
4.4 Bang-Bang Control, Sliding Modes


Lecture 5. Optimal Timing Problems and Optimal Feedback Control
5.1 Extremal Fields
5.2 Principle of Optimality, Hamilton-Jacobi-Bellman Equation
5.3 Optimal Switching and Timing Problems
5.4 Geometric Insight in Path Planning: Dubins, Naismith and Ulam's Problem.


Lecture 6. Linear Systems with Quadratic Criteria
6.1 Terminal Controllers: Soft Constraints
6.2 Terminal Controllers: Hard Constraints, LQ Paradox
6.3 LQ Regulator, Square Root Characteristic Equation, Spectral Factorization
6.4 The Riccati Equation


Prerequistes

 

Some knowledge of System Theory and Dynamics
A certain curiosity about mathematics and science in general.

 

Emphasis
Basic underlying principles in the theory and applications of optimiza-
tion and optimal control of systems.

 

Homework
A better understanding of the course materials will be gained by
working some problems.

 

References


Arturo Locatelli, Optimal Control, Birkhauser 2001.
J.L. Troutman, Variational Calculus and Optimal Control, 2-nd ed.
Springer Verlag, 1996.
A.E. Bryson and Y.-C. Ho, Applied Optimal Control: Optimization,
Estimation, and Control. Hemisphere, 1975.


Dates : November 19, 21, 24 and December 01, 03, 05, 2008

 

Schedule : 14h00 - 17 h00

 

Rooms
19/11 : 14h to 17h : Auditorium B

21/11 : 14h to 17h : local 02.54

24/11 : 14h to 17h : local 00.62

01/12 : 14h to 17h : local 00.62

!!! 03/12 : 13h to 16h30 : 00.62

!!! 05/12 : 13h to 16h30 : 00.62

 

This course will take place at the Katholieke Universiteit Leuven,
Department Elektrotechniek ESAT, Kasteelpark Arenberg 10, 3001 Heverlee

 

Paper 1.0, Paper 1.1, Paper 1.2, Paper 1.3, Paper Siam, Paper 2.1, Paper 2.2, Paper 2.3

 

 

4. SUBSPACE BASED IDENTIFICATION IN FREQUENCY DOMAIN AND MODELLING WITH ORTHONORMAL BASES FUNCTIONS

Lecturer : Huseyin AKCAY (Anadolu University, Turkey)

In this course, subspace-based identification algorithms for multi-variable systems from frequency response data are developed and their consistency properties are studied. These results are extended to infinite-dimensional systems. Also, subspace-based algorithms with power spectrum measurements are developed. Interpolation problems are studied and a subspace-based solution is proposed. Real world applications from mechanical engineering are discussed. Finally, orthonormal basis functions are introduced and their completeness and convergence properties are studied. Extensions to fractional linear systems are presented.

  

Contents

 

1. Subspace-based system identification in the frequency domain. Overview of methods for uniformly and non-uniformly spaced frequency response data. Consistency analysis and the effect of weighting. Real world applications.

 

2. Extensions to infinite-dimensional systems and time-domain implementations. Relations with balanced realizations and consistency.

 

3. Frequency domain subspace-based identification of discrete-time power spectra from non-uniformly spaced measurements.

 

4. Lagrange-Sylvester interpolation problems. A subspace-based solution. Applications to adaptive filtering /control and active control of vehicle suspensions.

 

5. Modelling with rational orthonormal basis functions. Completeness and convergence properties. Identification with orthonormal basis functions. Extensions to fractional systems. Synthesis of complete orthonormal fractional bases with arbitrary prescribed poles.

 

Prerequisites

 

Basic knowledge of linear algebra , calculus, and linear system theory .

 

Supporting material

 

Notes will be distributed during the course.

 

Related papers

 

1. Rik Pintelon and Johan Schoukens, ``System Identification: A Frequency Domain Approach’’, Wiley-IEEE Press, 2001.

2. Peter Van Overschee and Bart De Moor , `` Subspace Identification for Linear Systems’’, Kluwer Academic, 1996.

3. Tohru Katayama , `` Subspace Methods for System Identification’’ , Springer, 2005.

4 . Peter S.C. Heuberger, Paul M.J. Van den Hof, and Bo Wahlberg, `` Modelling and Identification with Rational Orthogonal Basis Functions’’, Springer, 2005.

 

Dates : February 09, 13, 16, 20, 23, 27, 2009.

 

Schedule : 09h15-12h15

 

This course will take place at CESAME, Bâtiment Euler, 4, av. G. Lemaître, 1348 Louvain-la-Neuve

 

Paper 1, Paper 2, Paper 3, Paper 4, Paper 5, Paper 6, Paper 7, Paper 8, Paper 9, lec2a, lec3a, lec4a, lec5a, lec8a, lec9a, lec9b, lec10a, lec10b, lec11a,

exam1, exam-sol1, HWI2, HWI-sol2, HWII2, HWII-sol2

 

 

5. "LINEAR AND NONLINEAR OBSERVERS WITH APPLICATIONS TO FAULT DETECTION AND ISOLATION "

Lecturers : Michel KINNAERT (ULB, Belgium) and Gildas BESANCON (INP Grenoble, France)

Contents

 

Course objective

 

The course aims at providing tools for estimation and monitoring purposes in linear and nonlinear dynamical systems, basically relying on so-called observers. The first 3 lectures provide an overview of observer design methods and the associated conditions of existence and convergence. The focus of the last 3 lectures is on fault detection and isolation in dynamical systems. This includes the generation of residuals, namely fault indicators, on the basis of the observer theory, and the processing of these signals in order to issue alarms and fault information.

 

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

 

First 3 lectures tought by Gildas Besançon, last 3 lectures by Michel Kinnaert

 

References

 

G. Besançon (Ed.), Nonlinear observers and applications, Lecture Notes in Control and Information Science 363, Springer Verlag, 2007

 

M. Blanke, M. Kinnaert, J. Lunze and M. Staroswiecki, Diagnosis and fault tolerant control , second edition, Springer, 2006.

 

M. Kinnaert, Fault diagnosis based on analytical models for linear and nonlinear systems – a tutorial. Session plénière. Actes de SAFEPROCESS 2003, juin 2003, Washington DC, pp 37-50.

 

Dates : April 20, 22, 24, 27, 29,30, 2009

 

Schedule : 9h15 - 12 h15

 

Rooms :


20/4       H2213 (building H, level 2, room 213)
22/4       UA5.104 (building U, door A, level 5, room 104)
24/4       UA5.104
27/4       H2213
29/4       UA5.104

30/4       UB5.230 (building U, door B, level 5 room 230)

 

For a map of the campus and for information on how to reach the campus, see

http://www.ulb.ac.be/docs/campus/solplan.html/

 

This course will take place at ULB, Campus du Solbosch CP 165/55, Avenue F.D. Roosevelt 50, 1050 Brussels

 

6. SOME TOPICS IN COMBINATORIAL OPTIMIZATION

 

Lecturers : Santanu Dey and Marco Di Summa (CORE, UCL)

 

In this course we will present some fundamental problems in combinatorial optimization. For each problem we will discuss applications and describe polynomial time combinatorial algorithms. Some polyhedral aspects will also be discussed.

 

Contents

  1. Lecture 1: Introduction, Cardinality Matching Problem.
  2. Lecture 2: Maximum Weight Matching Problem, Matching Polytope.
  3. Lecture 3: Matroid Greedy Algorithm, Matroid Polytope.
  4. Lecture 4: Matroid Intersection and Matroid Partitioning.
  5. Lecture 5: Submodular Function Minimization.
  6. Lecture 6: Approximation Algorithms: Edge Coloring, Traveling Salesman Problem.

 

Related books

 

Dates

 

The course will be held on alternate Wednesdays starting from February 4th, 2009 (Feb 4, Feb 18, March 4, March 18, April 1, April 15)

 

Schedule

 

2:00pm - 5:00pm

 

This course will take place at the CORE, room D.360, Voie du Roman Pays 34, 1348 Louvain-la-Neuve Belgium

 

 

Registration

You can register electronically by filling in the following form via the web :

http://www.uclouvain.be/sites/socn/graduate_registration.html

If you have problems with this, please contact Lydia DE BOECK

The admission is free for doctoral students and participants from Belgian academic institutions. Other participants are requested to pay a registration fee of EURO 500,- per course but a waiver can be obtained under special conditions (contact the secretariat).
Payment can be made by bank transfer to the account n°310-0959001-48 with the mention "AUTO2866 ACTIVITES DIDACTIQUES"

 

Secretariat

Lydia DE BOECK
CESAME - Bât. Euler
4, av. G. Lemaître
1348 Louvain-la-Neuve (Belgium)

 

Tél : 010/47 80 36

fax : 010/ 47 21 80

e-mail : lydia.deboeck@uclouvain.be

web site : http://www.uclouvain.be/sites/socn