Noninear Systems and Chaos

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

This advanced course will cover modern methods in nonlinear systems theory and applications. Basic feature of nonlinear systems theory is that state space approach is prevailing and frequency response methods are not generally applicable. The course will cover the topic: state model of nonlinear dynamical systems and its analysis, Lyapunov's stability, asymtotic stability and Lyapunov's methods, control synthesis via approximate linearization, high gain observers, gain scheduling. The main stress is on the so-called structural methods for the nonlinear control design, i.e. study of the system structural properties allowing easier applications of known control methods. That would consist of basics of differential geometry, Lie derivative, various types of exact feedback linearization, input-output linearization, zero dynamics, minimum phase systems, MIMO systems, decoupling. Last but not least, the course will provide verz basci information about chaotic systems including some motivating examples.

Requirements:

Prerequisites for this course is good knowledge of basics of control systems (frequency response, feedback, stability, PID regulation,...), then good knovledge of advanced course of linear control introducing notions like controllability, observability, minimal realization. Examples of these course are Automatic control and dynamical systems theory teache at CTU. last but not least, good knowledge of linear algebar (eigenvectors, eigenvalues, canonical forms of matrices,...) and mathematical analysis (differential calculus of more variables) are required.

Syllabus of lectures:

1. State space model of nonlinear dynamical system, typical nonlinear phenomena, examples.State space model of nonlinear dynamical system, typical nonlinear phenomena, examples.

2. Further practical examples of nonlinear dynamical systems. Chaotic systems.

3. Mathematical basics. Existence and uniqueness of solutions, dependence on initial conditions and parameters..

4. Definitions and methods of stability analysis. Ljapunov's function method and approx. linearization method.

5. Analysis of stability of perturbed asymptotically and exponentially stable systems.

6. Control synthesis via approximate linearization and obust linear methods. High gain observers.

7. Control synthesis via approximate linearization and gain scheduling.

8. Structural methods in nonlinear control synthesis - basic notions, exact transformations of nonlinear systems.

9. Structural methods and various types of exact linearization. Zero dynamics and minimum phase.

10. Structural methods and some basics of differential geometry and advanced analysis.

11. SISO systems. Relative degree. Input-output linearization. Zero dynamics, minimum phase systems.

12. MIMO systems I. Vector relative degree. Input-output linearization.

13. MIMO systems. Zero dynamics, minimum phase systems.

14. MIMO systems. Decoupling.

Syllabus of tutorials:

1. Example of nonlinear models and their simulations.

2. Laboratory examples of nonlinear systems.

3. Setting of individual long term homeworks for analysis and design of nonlinear systems control.

4. Sustems modelling

5. Modeling and simulation model design

6. Nonlinear systems simulations

7. Analysis of stability

8.Desing tasks and algorithms of control

9. Realization of control algorithms

10. Verification of control algorithms on simulation models

11. Exact feedback linearization design

12. Exact feedback linearization design - MIMO systems

13. Realization of controllers based on Exact feedback linearization design

14. Defense of results of long term homework

Study Objective:

Study materials:

1.H. K. Khalil, Nonlinear Systems. Third edition. Prentice Hall 2002. ISBN 0-13-067389-7.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Kybernetika a robotika - Systémy a řízení_145356 (compulsory course of the specialization)