Chaos in Automatic Control: 1st Edition (Hardback) book cover

Chaos in Automatic Control

1st Edition

Edited by Wilfrid Perruquetti, Jean-Pierre Barbot

CRC Press

592 pages | 133 B/W Illus.

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Hardback: 9780824726539
pub: 2005-10-14
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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.

Table of Contents


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


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


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


About the Series

Automation and Control Engineering

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Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Electronics / General