Analysis and Control of Dynamic Systems presenting Nonlinear Behaviors, Uncertainties and Time-Delays

Universidade Estadual de Campinas (UNICAMP)

Loquen Thomas — 2008-09-16T13:51:03Z

Contributions : Analysis and design of control laws taking into account nonlinear behaviors, time-delays, switching and uncertainties; application to flexible structures.

The UNICAMP has a solid reputation in both graduate and undergraduate programs, being widely recognized as one of the top universities in Brazil for its research and development activities. Both FEEC (School of Electrical and Computer Engineering) and FEM (School of Mechanical Engineering) are known abroad and have good performance indices when compared to other international institutions.

The researchers directly involved are: Prof. Pedro Luis Dias Peres (FEEC), Prof. Juan Camino (FEM).

INRIA – Rocquencourt

Loquen Thomas — 2007-10-16T11:20:31Z

Contributions : Stability and performance analysis of time-delay and uncertain systems, problems of average consensus.
The activities will concern the team Sisyphe, whose goal is to develop and promote methods and applications for automatic control. The researcher directly involved is Dr. Pierre-Alexandre Bliman - France

Laboratoire des Signaux et Systèmes/Supelec-CNRS

Loquen Thomas — 2007-10-16T11:17:43Z

Contributions : Stability and performance analysis of time-delay systems; development of new models for dynamical interconnected networks.
The researcher directly involved is Dr. Silviu-Iulian Niculescu - France

Expected results

Loquen Thomas — 2007-10-16T07:57:35Z

Development of new theoretical (“integrative”) techniques and methods allowing the analysis and control design of systems presenting simultaneously nonlinearities, time-delays and uncertainties.
Development of computational algorithms and software packages (as Matlab toolboxes)
Application of the developed techiques to real processes (chemical and biotechnological) and systems (network traffic control, flexible structures).
Generation of joint publications in national and international journals and conferences. Interchange of students and possibly thesis co-orientation.

Methodology

Loquen Thomas — 2007-10-16T07:50:00Z

The development of the theoretical part will be based on the Lyapunov theory. In order to deal with the nonlinearities, quadratic (parameter dependent or not), polynomial and Lure type Lyapunov functions and functionals will be considered.

The delay phenomenon should be taken into account by using different techniques. The first technique consists in using the properties of the spectrum of the corresponding characteristic functions in the analysis (delay intervals and stability domains) or in the design (extensions of predictor and pole placement techniques). The second technique, which is a straightforward extension of the undelayed case, is to consider Lyapunov-Krasovskii and Razhumikin approaches. Another promising approach is to model the delay system as an uncertain system and to use robust control approaches to design efficient control laws (as, for example, the so-called “Integral Quadratic Constraints”, IQC setting). This approach has the advantage of naturally dealing with uncertain systems and performances issues. From the application of these functions and functionals, analysis and synthesis conditions in the form of linear matrix inequalities (LMIs), if possible, should be derived. This fact will allow the formulation of convex optimization problems for the analysis and design purposes. The most promising methods will be tested using simulated examples and also implemented in pilot plants in order to asset their performance under real conditions. All the developments will follow basically 5 steps: literature review of existing methods, theoretical formulations, development of computational algorithms, tests and performances evaluation in simulation, application to real processes and systems covering the examples mentioned above.

Project scope

2007-10-16T07:43:34Z

The considered nonlinearities will be associated to 2 classes.

The first one regards the dynamical behavior of nonlinearities and we will be particularly interested in systems that can be put in a rational form, in a Lure form or even in a Linear Parameter-Varying (LPV) form. The second one considers the hard-nonlinearities such as saturations (both in amplitude and rate of states, control or output signals), positivity constraints, hysteresis as well as switching behaviors. Concerning the delays, different types of delays will be considered. The first classical approach considers the delay as constant but uncertain belonging to a prescribed range. Even if extensively studied in the last few years, several questions are still open like ensuring the stabilization in a range for an uncertain system or the output feedback stabilization. Delays are sometimes accompanied “interference” (multiple independent delays) and “quenching” phenomena (time-varying delays), which lead to degrading properties of the corresponding systems. Such phenomena need a better theoretical comprehension together with appropriate analysis tools. A more general modeling approach considers systems presenting uncertain time-varying delays in the state and/or in the input/output. An important concern in this case will be to provide constructive methods to design controllers which ensure the robust stabilization of a time varying delay system, whose delay variation rate is uncertain. Furthermore, the class of considered uncertainties will be of LFT type in systems parameters. Considering these characteristics in an analysis context, the goal consists in providing methods for estimating the region of attraction of the closed-loop systems as well as the bounds on tolerated external disturbances, delays and uncertainties for which the closed-loop desired properties are ensured. In a control design context, the idea is to develop methods enabling the design of stabilizing control laws (both in global and local contexts) associated to the optimization of performance measures, disturbance rejection and size of the region of attraction. For application purposes, special attention will be given to the development of output feedback control laws (both dynamical and static), model predictive control, anti-windup strategies or still hybrid control (i.e., based on both continuous and discrete parts).

Goals

2007-10-16T07:28:08Z

The main goal of the present project is the development of new modeling and control methods to take into account nonlinearities, delays and uncertainties in dynamical systems.

In this context, the integration of different techniques and approaches to deal with these issues will be given a special attention. These developments will be focused directly on solving real problems from different areas such as: process control, flexible structures, communication network control and control over communication networks. All these areas are important examples of systems presenting simultaneously all the features to be studied in this project. In parallel, the project aims at interchanging experiences and techniques among the participants, involving students (PhD. and Msc.) in research and developments as well as generating joint publications in international journals and conferences.

Abstract

Loquen Thomas — 2007-10-16T07:22:56Z

The proposed project is concerned with the development of new modeling and control methods to take into account nonlinearities, delays and uncertainties in dynamical systems.

The goal is to propose new theoretical conditions for analysis and control design, providing less conservative solutions than the ones found so far in the literature. The basis for this work are the recent advances in Lyapunov theory, namely the use of polynomial and parameter dependent Lyapunov functions and functionals, as well as in the modeling of nonlinear systems (generalized sector conditions, rational forms) and uncertainties. The required theoretical conditions will be stated under the form of linear matrix inequalities (LMIs) allowing the formulation of optimization problems in order to compute: estimates of the region of attraction; tolerated bounds on disturbances, delays and uncertainties; robust stabilizing (local and global) control laws ensuring good performance and disturbance rejection levels. These developments will be directly focused on real applications in the areas of process control, flexible structures, communication networks, and control over distributed communication networks. This research proposal provides an exciting and fertile ground for increasing the collaboration among the participants and enhancing their postgraduate programs.

LAAS-CNRS

2007-10-12T07:12:14Z

Contributions : Developments of control laws taking into account delays, saturations, switching and robustness issues; stability and performance analysis of time-delay systems; applications to biotechnological processes and flexible structures.

The activities will be developed in the group MAC (Methods and Algorithms for Control), which is a leading group in robust and saturated systems.

The researchers directly involved are: Dr. Sophie Tarbouriech, Prof. Germain Garcia, Prof. Frederic Gouaisbaut, Dr. Christophe Prieur, Dr. Isabelle Queinnec, Thomas Loquen (PhD. Student.), Yassine Ariba (Phd Student.), Giorgio Valmorbida (PhD. Student)

Introduction

Loquen Thomas — 2007-10-12T06:53:54Z

STIC-South America is a scientific-technological cooperation programme integrated by France, Argentine, Brazil, Chile, Peru and Uruguay.

The aim of the project is to promote and strengthen South America regional capacities and their cooperation with France, towards the settlement of research and development webs on Science, Information Technology and Communication field.

On this scope, the programme convokes to select and sponsor research and development projects, which are able to transfer innovation proposals at a regional level. These projects, which have a maximum extension of two years, include at least two countries of the region and one or more French scientific team(s).

http://www.sticamsud.org/english/Main/Inicio