Provides an integrated reference to the analysis, design, and applications of chaos in control systemsTakes a deterministic approach based on ordinary differential and difference equationsIntroduces chaos theory progressively from bifurcation theory and singular perturbation to normal formsExamines synchronization, observability bifurcation, chaotic and hyperchaotic control, and control bifurcationIncludes more than 130 figures and 1140 equations to illustrate the concepts
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