Graduate school courses

2005 - 2006

 

 

 

1. SYNCHRONISATION AND CONTROL

Lecturers : H. Nijmeijer and A.Yu. Pogromsky (Eindhoven University of Technology, The Netherlands)


Contents :

Part I Introduction

Part II An observer view on synchronization

Part III Controlled synchronization

Part IV (Partial) synchronization in diffusive networks

Part V Communication and synchronization

Part VI Coordination of mechanical systems

The subject of the course has become very popular in the last decades. First, mostly from a physics/biology viewpoint studies focussed on how synchronization arises in coupled systems. More recently, the subject also is receiving considerable attention in the control community and also captures the study of coordination of large sets of actuators. From a control perspective synchronization has much in common with the observer problem, and this viewpoint will be extensively used during the course. Controlled synchronization combines feedback control with observer theory.
As part of the course, students will work on a number of illustrative hand-out exercises.

 
Dates : October 07 - 14 - 28 , 2005.

Schedule : 10h -13h and 14h30 - 17h30


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

 

Material of the course

Paper1, Paper2, Paper3, Paper4, Paper5, Paper6, Paper7, Paper8, Paper9, Slides

 



2. INDEPENDENT COMPONENT ANALYSIS AND BLIND IDENTIFICATION/DECONVOLUTION

 

Lecturers : P. Comon (Laboratoire I3S, France), L. De Lathauwer (Laboratoire ETIS, France) and F. Desbouvries (Institut National des Télécommunications, France)

 

Contents :

Independent Component Analysis (ICA) and Blind Source Separation (BSS) consist of the separation of an instantaneous mixture of unknown statistically independent random variables, without prior knowledge of the mixing coefficients. Blind identification/deconvolution concerns the estimation/equalization of an unknown convolutive mixing. In the last decade, these topics have emerged as new key concepts, with many applications, in signal processing (e.g.digital communications), data analysis and system identification.

Required mathematical tools, like higher-order statistics and some concepts of multilinear algebra, will be properly introduced. A conceptual discussion of ICA will cover uniqueness aspects, relationship with PCA, over- vs. underdetermined mixtures, contrast functions, etc. In its basic form, ICA exploits the statistical independence of non-Gaussian signals. Variants are based on differences in spectral color or nonstationarity. Several key algorithms of these different classes will be discussed in detail. Approaches with and without prewhitening will be compared. Special attention will be paid to the blind identification of underdetermined mixtures, where the number of observation channels is strictly smaller than the number of independent components. Both instantaneous and convolutive mixtures will be dealt with. Many second-order blind identification methods were initially derived from the algebraic properties of structured matrices, and further developed and extended using tools coming from multidimensional system theory. Here too, the course will first recall the necessary background, and next focus on the application to blind identification.

Closely related to ICA are methods for the blind separation/deconvolution of deterministic signals, based on the presumed algebraic properties of the latter. Both for instantaneous and convolutive methods, a number of important algorithms will be discussed.

 

Prerequisites :

Basic knowledge of matrix algebra.

 

Supporting material :

Lecture notes will be distributed during the course.

 

Evaluation :

Two alternatives are offered for evaluation of this course :
1. Application of a selected number of methods, discussed during the course, to a problem of choice (e.g. related to the students Ph.D. subject). Discussion of the results in a short report (5-10 pages).
2. A multiple choice quiz-like test.

 

Dates : November 16-17-24-25-28 and December 05, 2005

 

Schedule : 14h - 17 h

 

Rooms :

16/11 : ESAT, room 02.58

17/11: Auditorium A (ESAT Building)

24-25-28/11 and 5/12 : Room 00.62


This course will take place at the Department of Mechanical Engineering, Katholieke Universiteit Leuven,
Celestijnenlaan 300B, 3001 Heverlee


3. REGULATOR TUNING METHODS

Lecturers : A. Bazanella (Federal University of Rio Grande do Sul, Brazil) and M. Gevers (CESAME, UCL, Belgium)

 

This course will present theoretical and practical aspects of regulator tuning methods based on experiments on the process to be controlled. The major part of the course will focus on tuning methods based on relay feedback experiments, both for single-input single-output (SISO) and for multi-input (MIMO) processes. The last part of the course will focus on the Iterative Feedback Tuning (IFT) method, which is an optimal control method using a regulator of fixed structure. IFT also uses a feedback experiment on the process, in order to generate an unbiased estimate of the gradient of the control performance criterion. The course aims at PhD students with an interest in control design methods as well as control engineers. The main theme of the course is online estimation of process characteristics and regulator tuning for enhanced performance.

 

Contents :

1. Preliminaries. Review of SISO control analysis tools: the Nyquist stability criterion; stability margins; basic results in performance of PID-controlled loops; the describing function method. Critical quantities of a process and related PID tuning formulae (Ziegler-Nichols, Tyreus-Luyben, etc): definitions, performance analysis and robustness analysis. Basic regulator tuning based on partial knowledge of the frequency response. The relay feedback experiment for estimation of critical quantities: definitions and motivation.

2. The standard relay feedback experiment. Approximate analysis through the describing function method: existence, uniqueness, frequency, amplitude and stability of limit-cycles; improved estimates. Exact analysis through Poincaré maps: existence, uniqueness, frequency, amplitude and stability of limit-cycles; existence of strange phenomena: fast switching and chaos.

3. Frequency response estimation with relay experiments. Nonstandard relay experiments: definitions and applications. Analysis of the Arruda-Barros relay experiment and applications. Direct estimation of stability margins. Design criteria based on partial knowledge of the frequency response.

4. Tuning of decentralized MIMO regulators. Regulator tuning for diagonally dominant processes: estimation of coupling norms, detuning. Sequential tuning of control loops. MIMO systems analysis: the MIMO Nyquist criterion, critical quantities of a MIMO process, characterization of critical surfaces in the parameter space.

5. Estimation of critical quantities by decentralized relay feedback. MIMO regulator tuning formulae based on critical quantities. Practical aspects in auto-tuning. Relay bias calculation, parameter (relay's amplitude and hysteresis) determination, diagnosis of poor performance to trigger auto-tuning.

6. Iterative Feedback Tuning. Presentation of the IFT method, based on feedback experiments applied to the process in order to generate estimates of the gradient of the cost function. Application examples. Recent developments of the IFT method: optimal filtering to reduce the variance of the gradient estimate; generation of an unbiased estimate of the Hessian; modification of the IFT criterion for robustness; etc.

 

Supporting material :

Lecture notes and several journal articles will be distributed during the course.

 

Prerequisites :

Basic knowledge of linear systems and control theory.

 

Evaluation :

Two individual projects will be assigned to each student.

 

Dates : February 13-20-27 and March 06-16-20, 2006.

 

Schedule : 9h -12h30


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



4. CONVEX OPTIMIZATION

Lecturer : L. Vandenberghe (University of California Los Angeles, USA)

 

The course will offer an introduction to the basic theory, engineering applications, and numerical algorithms of convex optimization. The focus will be on convex modeling, i.e., recognizing and formulating convex optimization problems in applications, and on practical methods for solving convex optimization problems.

 

Topics :

1. Convex sets and functions.

2. Convex optimization problems. Linear and quadratic programming.
Geometric programming. Second-order cone and semidefinite programming.

3. Duality and optimality conditions.

4. Applications in control, signal processing, circuit design, statistics,
computational geometry.

5. Algorithms for unconstrained optimization.

6. Interior-point methods for constrained optimization.

 

Supporting material :

The course will based on the book Convex Optimization by
S. Boyd and L. Vandenberghe (www.ee.ucla.edu/~vandenbe/cvxbook.html).

Additional lecture notes will be made available during the course.

 

Prerequisites : Good knowledge of linear algebra.

 

Dates :
April 24 (9h00-12h30)
May 02 (8h30 - 12h30) : Auditorium de Molen - MOLE 00.07
May 08 (8h30 - 12h30) : Auditorium van het Arenberg kasteel - KAST 01.07
May 15 (8h30 - 12h30) : Auditorium de Molen - MOLE 00.07
May 22 (8h30 - 12h30) : Auditorium van het Arenberg kasteel - KAST 01.07
May 29 (8h30 - 12h30) : Auditorium van het Arenberg kasteel - KAST 01.07

This course will take place at the Department of Mechanical Engineering, Katholieke Universiteit Leuven,
Celestijnenlaan 300B, 3001 Heverlee

5. LMI OPTIMIZATION WITH APPLICATIONS IN CONTROL

Lecturer : Didier Henrion (LAAS-CNRS, Toulouse, France, and FEL-CVUT, Prague, Czech Republic)

 

This course is organized by the ICCoS (Identification and Control of Complex Systems) Scientific Research Nework of the Research Foundation - Flanders (FWO- Vlaanderen),and the K.U. Leuven -BOF EF/05/006 Center of Excellence on Optimization in Engineering

 

Outline :

The course starts with basic mathematical features of linear and bilinear matrix inequalities:

Then the course focuses on the application of LMI techniques to solve several control problems traditionally deemed as difficult, such as robustness analysis of linear and nonlinear systems, or design of fixed-order robust controllers with H-infinity specifications. The originality of the approach is in the simultaneous use of algebraic or polynomial techniques (as opposed to classical state-space methods) and modern convex optimization techniques:


For the labs we use the YALMIP interface, SeDuMi and PENBMI to define and solve LMI and BMI problems under the Matlab environment (3h).

 

Dates : Thursday, June 1 and Friday, June 2, 2006

 

Schedule : It consists of six 90-minute lectures (9:00-10:30, 11:00-12:30, 14:00-15:30, 16:00-17:30 on June 1, 9:00-10:30, 11:00-12:30 on June 2) and one 3-hour lab (14:00-17:00 on June 2).

 

This course will take place at the Department of Mechanical Engineering, Katholieke Universiteit Leuven,
Celestijnenlaan 300B, 3001 Heverlee