1st Edition

Chaos in Automatic Control

Edited By Wilfrid Perruquetti, Jean-Pierre Barbot Copyright 2006
    592 Pages 133 B/W Illustrations
    by CRC Press

    Chaotic behavior arises in a variety of control settings. In some cases, it is beneficial to remove this behavior; in others, introducing or taking advantage of the existing chaotic components can be useful for example in cryptography. Chaos in Automatic Control surveys the latest methods for inserting, taking advantage of, or removing chaos in a variety of applications. This book supplies the theoretical and pedagogical basis of chaos in control systems along with new concepts and recent developments in the field.

    Presented in three parts, the book examines open-loop analysis, closed-loop control, and applications of chaos in control systems. The first section builds a background in the mathematics of ordinary differential and difference equations on which the remainder of the book is based. It includes an introductory chapter by Christian Mira, a pioneer in chaos research. The next section explores solutions to problems arising in observation and control of closed-loop chaotic control systems. These include model-independent control methods, strategies such as H-infinity and sliding modes, polytopic observers, normal forms using homogeneous transformations, and observability normal forms. The final section explores applications in wireless transmission, optics, power electronics, and cryptography.

    Chaos in Automatic Control distills the latest thinking in chaos while relating it to the most recent developments and applications in control. It serves as a platform for developing more robust, autonomous, intelligent, and adaptive systems.

    OPEN-LOOP ANALYSIS
    Bifurcation and Chaos in Discrete Models: An Introductory Survey; C. Mira
    Tools for Ordinary Differential Equations Analysis; W. Perruquetti
    Normal Forms and Bifurcations of Vector Fields; C. Dang Vu-Delcarte
    Feedback Equivalence of Nonlinear Control Systems: A Survey on Formal Approach; W. Respondek and I.A. Tall
    Singular Perturbation and Chaos; M. Djemai and S. Ramdani

    CLOSED-LOOP DESIGN
    Control of Chaotic and Hyperchaotic Systems; L. Laval
    Polytopic Observers for Synchronization of Chaotic Maps; G. Millérioux and J. Daafouz
    Normal Forms of Nonlinear Control Systems; W. Kang and A.J. Krener
    Observability Bifurcations: Application to Cryptography; J-P. Barbot, I. Belmouhoub, and L. Boutat-Baddas
    Nonlinear Observer Design for Smooth Systems; A.J. Krener and M. Xiao

    SOME APPLICATIONS
    Chaos and Communications; R. Quéré, J. Guittard, and J.C. Nallatamby
    Chaos, Optical Systems, and Application to Cryptography; L. Larger
    Indirect Field-Oriented Control of Induction Motors: A Hopf Bifurcation Analysis; F. Gordillo, F. Salas, R. Ortega, and J. Aracil
    Implementation of the Chua's Circuit and its Application in the Data Transmission; L. Boutat-Baddas, J-P. Barbot, and R. Tauleigne
    Synchronization of Discrete-Time Chaotic Systems for Secured Data Transmission; I. Belmouhoub and M. Djemai
    Appendix A. On Ergodic Theory of Chaos
    INDEX

    Biography

    Wilfrid Perruquetti, Jean-Pierre Barbot