Zhang / Liu / Wang Controlling Chaos

Suppression, Synchronization and Chaotification
1. Auflage 2009
ISBN: 978-1-84882-523-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 344 Seiten

Reihe: Communications and Control Engineering

Controlling Chaos achieves three goals: the suppression, synchronisation and generation of chaos, each of which is the focus of a separate part of the book. The text deals with the well-known Lorenz, Rössler and Hénon attractors and the Chua circuit and with less celebrated novel systems. Modelling of chaos is accomplished using difference equations and ordinary and time-delayed differential equations. The methods directed at controlling chaos benefit from the influence of advanced nonlinear control theory: inverse optimal control is used for stabilization; exact linearization for synchronization; and impulsive control for chaotification. Notably, a fusion of chaos and fuzzy systems theories is employed. Time-delayed systems are also studied. The results presented are general for a broad class of chaotic systems. This monograph is self-contained with introductory material providing a review of the history of chaos control and the necessary mathematical preliminaries for working with dynamical systems.

Autoren/Hrsg.

Zhang, Huaguang

Liu, Derong

Wang, Zhiliang

Inhaltsverzeichnis

1;Foreword;7
2;Preface;9
3;Contents;15
4;Chapter 1 Overview;20
4.1;1.1 The Origin and Development of Chaos Theory;20
4.2;1.2 Control of Chaos;22
4.3;1.3 Anticontrol of Chaos;29
4.4;1.4 Summary;31
4.5;References;32
5;Chapter 2 Preliminaries of Nonlinear Dynamics and Chaos;35
5.1;2.1 Introduction;35
5.2;2.2 Background;36
5.3;2.3 Existence, Uniqueness, Flow, and Dynamical Systems;38
5.4;2.4 Equilibrium, Periodic Orbit, Quasiperiodic Orbit, and Poincar´e Map;42
5.5;2.5 Invariant and Attracting Sets;47
5.6;2.6 Continuous-Time Systems in the Plane;49
5.7;2.7 General Solutions of Discrete-Time Linear Systems;55
5.8;2.8 Discrete-Time Systems in the Plane;56
5.9;2.9 Stabilities of Trajectories I: The Lyapunov First Method;61
5.10;2.10 Stabilities of Trajectories II: The Lyapunov Second Method;68
5.11;2.11 Chaotic Sets and Chaotic Attractors;71
5.12;2.12 Symbolic Dynamics and the Shift Map;72
5.13;2.13 Lyapunov Exponent;75
5.14;2.14 Examples;77
5.15;2.15 Basics of Functional Differential Equations Theory;89
5.16;2.16 Summary;93
5.17;References;94
6;Chapter 3 Entrainment and Migration Control of Chaotic Systems;95
6.1;3.1 Introduction;95
6.2;3.2 Basics on Entrainment and Migration;96
6.3;3.3 OPCL Control Scheme;102
6.4;3.4 Global Control of a Class of Continuous-Time Polynomial Chaotic Systems;103
6.5;3.5 Global Control of a Class of Discrete-Time Systems;113
6.6;3.6 Summary;119
6.7;References;120
7;Chapter 4 Feedback Control of Chaotic Systems;121
7.1;4.1 Introduction;121
7.2;4.2 Model-Reference Adaptive Control of a Class of Discrete-Time Chaotic Systems;122
7.3;4.3 Model-Reference Adaptive Control of a Class of Continuous-Time Chaotic Systems;129
7.4;4.4 Control of a Class of Chaotic Systems Based on Inverse Optimal Control;143
7.5;4.5 Summary;148
7.6;References;149
8;Chapter 5 Synchronizing Chaotic Systems Based on Feedback Control;150
8.1;5.1 Introduction;150
8.2;5.2 Synchronization of Continuous-Time Chaotic Systems with a Single Input;151
8.3;5.3 Synchronization of Multi-Signals in Continuous-Time Chaotic Systems;159
8.4;5.4 Synchronization of Different Continuous-Time Chaotic Systems;167
8.5;5.5 Synchronization of Discrete-Time Chaotic Systems;174
8.6;5.6 Summary;184
8.7;References;185
9;Chapter 6 Synchronizing Chaotic Systems via Impulsive Control;186
9.1;6.1 Introduction;186
9.2;6.2 Complete Synchronization of a Class of Chaotic Systems via Impulsive Control;187
9.3;6.3 Lag-Synchronization of the Unified Systems via Impulsive Control;197
9.4;6.4 Impulsive Synchronization of Different Chaotic Systems;204
9.5;6.5 Impulsive Synchronization of a Class of Chaotic Delayed Neural Networks;215
9.6;6.6 Summary;223
9.7;References;223
10;Chapter 7 Synchronization of Chaotic Systems with Time Delay;225
10.1;7.1 Introduction;225
10.2;7.2 Adaptive Synchronization of a Class of Delayed Chaotic Systems;226
10.3;7.3 Adaptive Synchronization Between Two Different Delayed Chaotic Systems;237
10.4;7.4 Synchronization of Chaotic Delayed Neural Networks;254
10.5;7.5 Summary;282
10.6;References;283
11;Chapter 8 Synchronizing Chaotic Systems Based on Fuzzy Models;284
11.1;8.1 Introduction;284
11.2;8.2 Modeling Chaotic Systems via T–S Fuzzy Models;285
11.3;8.3 Synchronization of Hyperchaotic Systems via T–S Fuzzy Models;292
11.4;8.4 Synchronizing Fuzzy Chaotic Systems with Time-Varying Delays;313
11.5;8.5 Summary;321
11.6;References;321
12;Chapter 9 Chaotification of Nonchaotic Systems;323
12.1;9.1 Introduction;323
12.2;9.2 Chaotification of Discrete-Time Fuzzy Hyperbolic Model with Uncertain Parameters;324
12.3;9.3 Chaotification of Continuous-Time Fuzzy Hyperbolic Model Using Impulsive Control;332
12.4;9.4 Chaotification of Linear Systems Using Sampled Data Control;341
12.5;9.5 Summary;353
12.6;References;354
13;Index;356