Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. There exists no similar control theory-oriented book available in the market that is devoted to the subject of chaos control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The new technology of chaos control has major impact on novel engineering applications such as telecommunications, power systems, liquid mixing, internet technology, high-performance circuits and devices, biological systems modeling like the brain and the heart, and decision making. The book is not only aimed at active researchers in the field of chaos control involving control and systems engineers, theoretical and experimental physicists, and applied mathematicians, but also at a general audience in related fields.
Author(s): Guanrong Chen, Xinghuo Yu
Series: Lecture Notes in Control and Information Sciences
Edition: 1
Publisher: Springer
Year: 2003
Language: English
Pages: 343
Tags: Математика;Нелинейная динамика;
front-matter......Page 1
1 Introduction: Is “Controlling Chaos” an Oxymoron?......Page 10
2 Statement of the Targeting Problem......Page 11
3 Targeting: A Simple and Instructive One-Dimensional Example......Page 13
3.1 The higher-dimensional generalization......Page 14
3.2 A web approach to higher-dimensional targeting......Page 15
3.3 Targeting through recurrence through resonance layers and to the moon......Page 16
4 Combinatorial Targeting and Symbolic Dynamics......Page 21
4.1 One-dimensional maps with a single critical point......Page 22
4.2 Higher-dimensional systems and symbolic dynamics of di.eomorphisms......Page 24
4.3 Learning the grammar in practice......Page 25
5 Forcing the Path: Feedback Control......Page 26
5.1 Parametric feedback control......Page 27
5.2 Time-delayed feedback control......Page 28
5.3 Dynamic limiting......Page 29
1 Introduction......Page 34
2 Linear Wave Equation with a van der Pol Boundary Condition......Page 38
3 Some Open Questions......Page 55
1 Introduction......Page 60
2 Hybrid Systems......Page 62
3.2 Generalization......Page 64
3.3 Convergence analysis......Page 65
4 Switched Arrival System......Page 67
5 Chua’s Circuit......Page 72
6 Conclusions......Page 76
References......Page 77
1 Introduction......Page 79
2.1 Stabilization of periodic orbits......Page 80
2.3 Discrete-time delayed feedback control......Page 81
3 The Odd Number Limitation......Page 82
3.1 The odd number limitation via discrete-time DFC......Page 83
3.3 Overcoming the odd number limitation......Page 84
4.1 Half-periodic DFC......Page 85
5 Dynamic DFC......Page 86
5.1 Observer-based DFC......Page 87
5.2 State feedback......Page 88
5.3 Extended DFC......Page 89
6 Recursive DFC......Page 90
7.1 Second-order dynamic delayed feedback controller......Page 91
7.2 Recursive delayed feedback controller......Page 92
References......Page 93
1.2 The perturbed nonlinear Schr¨odinger equation (NSL)......Page 96
1.4 The extended Fisber-Kolmogorov (F-K) equation......Page 97
2.1 The Lyapunov exponent method......Page 98
2.2 Measurement of chaos by entropy......Page 103
2.3 Perturbation theory and the Melnikov method......Page 104
2.4 Some numerical and analytic methods......Page 105
2.5 Use decay mutual information to characterize spatiotemporal chaotic dynamics.......Page 108
3 Controlling chaos to a class of PDEs by applying invariant manifold and structure stability theory......Page 109
Appendix......Page 120
References......Page 121
1 Introduction......Page 123
2 Master-Slave Synchronization: Autonomous Case......Page 124
2.2 Master-slave synchronization using dynamic output feedback......Page 126
2.3 Robust synchronization......Page 127
2.4 Synchronization with time delay......Page 128
3 Nonlinear H Synchronization......Page 130
4.1 Impulsive synchronization: state feedback case......Page 132
4.2 Impulsive synchronization: measurement feedback case......Page 133
5 Examples......Page 134
6 Conclusions......Page 137
References......Page 138
1 Introduction......Page 142
2 Inverse Optimal Control......Page 143
3.1 Mathematical description......Page 145
3.2 Model-following as a stabilization problem......Page 146
3.3 Inverse optimal control......Page 147
3.4 Chaos reproduction......Page 150
4 Chaos Synchronization via Adaptive Recurrent Neural Control......Page 152
4.1 Recurrent high-order neural network......Page 154
4.3 Tracking analysis......Page 155
4.4 Tracking error stabilization......Page 157
4.5 Inverse optimal control......Page 158
4.6 Chaos synchronization......Page 159
5 Conclusions......Page 161
1 Introduction......Page 164
2.2 Chaos in the sense of Li-Yorke......Page 166
3 Chaotification: Problem Formulation......Page 168
4 An Illustrative Example......Page 173
5 Some Remarks on the Continuous-Time Case......Page 178
6 Concluding Remarks......Page 179
References......Page 180
1 Introduction......Page 183
2.1 Generating chaos in a linear diffential equation......Page 184
2.3 Generating chaos in feedback linearizable systems......Page 186
3.1 Normal form of chaotic systems......Page 192
3.2 Generating chaos in linear controllable systems......Page 196
3.3 Generating chaos in feedback linearizable systems......Page 198
3.4 Generating chaos in feedback unlinearizable systems......Page 200
4 Generating Chaos in Continuous-Time Systems Using Impulsive Control......Page 204
5 Conclusions......Page 206
References......Page 207
1 Introduction......Page 209
2 Pseudo-Random Number Generators......Page 210
3 Algorithmic Complexity and Randomness......Page 212
4 Computational Complexity and Randomness......Page 213
5 Determinism, Chaos and Randomness......Page 216
6 Shadowing......Page 219
7 Chaos-Based Pseudo-Random Number Generators......Page 220
References......Page 224
1 Introduction......Page 227
2.1 Category I: Modulation based on the chaotic signals......Page 230
2.2 Category II: Modulation based on chaotic state functions......Page 233
2.3 Category III: Modulation based on the system parameters......Page 237
3.1 An ergodic approach to chaos communication......Page 238
3.2 System model of E-DCSK......Page 240
3.3 BER of E-DCSK......Page 241
4.1 Noise performance in an AWGN channel......Page 244
4.2 BER performance of E-DCSK under special noise environment......Page 251
5 Conclusions......Page 254
1 Introduction......Page 257
2 Some Tools for Computing Expectations of Quantized Chaotic Trajectories......Page 260
3 Asynchronous DS-CDMA Systems Model......Page 266
4 System Performance Merit Figure......Page 269
5 Performance Optimization in Dispersive and Non-Dispersive Channels A......Page 271
6 Chaos-Based Generation of Optimized Spreading Sequences......Page 273
7 Chaos-Based DS-CDMA System Prototype and Measurement Results......Page 275
7.2 Performance over exponential channel......Page 278
8 Conclusions......Page 279
References......Page 280
1 Introduction......Page 283
2 Piecewise ACne Systems......Page 284
3 Piecewise Smooth Systems......Page 285
4.1 Formulation......Page 287
4.2 Repetitive calculation of UPOs embedded in a chaotic attractor......Page 289
4.3 Calculation of UPOs in a piecewise smooth system......Page 291
5.1 Stability analysis of EFC for piecewise smooth systems......Page 295
5.2 EFC for piecewise smooth systems......Page 298
6 Conclusions......Page 300
References......Page 301
1 Introduction......Page 303
2.1 The particle-core model......Page 305
2.2 Breathing model interaction with particle motion......Page 306
2.3 Nonlinear resonances and induced chaos......Page 310
2.4 Halo formation in three-dimensional bunches......Page 313
2.5 Canonical transformation method......Page 319
2.6 The matrix transfer method......Page 323
3 Nonlinear Feedback Control of Beam Halo Chaos in PFCs......Page 325
4 Wavelet-Based Feedback Control......Page 328
4.1 Main control results via wavelet-based feedback......Page 329
5 Switching Manifold Control Method......Page 333
6 Time-Delayed Self-Control Feedback Method......Page 337
7 Conclusions and Discussions......Page 340
