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Tables of Contents for From Chaos to Order
Chapter/Section Title
Page #
Page Count
Foreword
vii
Preface
ix
Acknowledgments
xii
Introduction
1
20
Controlling Chaos
2
12
Chaos Control -- in a Broader Sense
2
1
Why Chaos Control?
3
3
Early Skepticism and Recent Effort
6
2
Chaos Control -- Two Examples
8
6
Some Distinct Features of Chaos Control
14
2
Organization of the Monograph
16
5
Nonlinear Dynamical Systems
21
68
Nonlinear Dynamical Systems
22
12
Nonlinear Dynamical System Preliminaries
23
4
Periodic Orbits and Limit Cycles
27
2
Limit Sets and Attractors
29
2
Poincare Maps
31
1
Homoclinic and Heteroclinic Trajectories
32
2
Some Analytical Tools
34
7
Center Manifold Theory
35
1
Poincare's Normal Forms
36
1
Delay-Coordinates and Embedology
37
4
Chaos in Nonlinear Systems
41
25
What Is Chaos?
42
1
Features of Chaos
43
16
Bifurcations
59
7
A World of Chaos
66
18
Chaos is Ubiquitous
67
1
Paradigms of Chaos
67
17
Symmetry, Self-Similarity, and Stabilities
84
5
Symmetry and Self-Similarity
84
1
Stabilities
85
4
Parameter-Dependent Approaches to Chaos Control
89
46
Periodic Parametric Forcing
90
6
Parametrically Forced Oscillators
91
3
Parametrically Forced Convective Flows
94
2
Microscopic Parametric Variation
96
30
The Original Approach
97
7
Some Experimental Studies
104
5
Convergence Analysis
109
2
Targeting
111
3
Using the Delay-Coordinates Technique
114
3
Controlling Chaos to Higher-Periodic Orbits
117
2
A Modification of the Original Method
119
3
Some Applications of Parametric Variation Control
122
1
Controlling Transient Chaos
123
3
Parameter Tuning and Chaos Control
126
6
Controlling Chaos Onset via Parameter Tuning
127
2
Controlling the Size of a Chaotic Attractor
129
1
Parameter Tuning Based on Bifurcation Analysis
130
1
Some Applications of Parameter Control
131
1
Summary
132
3
Open-Loop Strategies for Chaos Control
135
38
Chaos Control via External Forcing
136
12
Using External Weak Periodic Force
136
3
Local Stability Analysis
139
2
Phase Effect in External Weak Forcing Control
141
5
Using Random Noise as Control Force
146
1
Using Periodic Impulse Input as Control Force
147
1
Entrainment and Migration Controls
148
23
Entrainment-Goal Control
149
11
Migration-Goal Control
160
5
Entrainment and Migration with Feedback
165
6
Summary
171
2
Engineering Feedback Control (I)
173
64
Chaos in Feedback Control Systems
175
15
Chaos in Continuous-Time Feedback Systems
176
7
Chaos in Discrete-Time Feedback Systems
183
7
Automatic Systems Control
190
9
Engineering Control Using Feedback
190
4
Feedback Versus Open-Loop Controls
194
1
Some Practical Perspectives
195
3
Feedback Control of Chaos
198
1
Chaos Control vis Lyapunov Methods
199
32
Lyapunov Theorems
201
5
Controlling Chaos via Lyapunov Methods
206
22
Controlling Chaos to Higher-Periodic Orbits
228
3
Some General Controllability Conditions
231
3
Summary
234
3
Engineering Feedback Control (II)
237
56
Optimal Control of Chaos
237
17
Optimal Controls
238
3
A Case of Optimal Control of Chaos
241
2
Optimal Parametric Variation Control
243
3
Comparison of Optimal Chaos Control Strategies
246
4
H∞-Control Approach
250
4
Toward Robust Control of Chaos
254
11
Chaotic Vibration Control
255
4
A Two-Degree-of-Freedom Controller
259
6
Contraction Mapping and Sliding Mode Controls
265
9
Contraction Mapping Based Control
265
4
Sliding Mode Control
269
4
Control of Systems with Discontinuous Vector Fields
273
1
Discretization Chaos and Its Control
274
17
Chaos From Discretization
275
2
Chaos Suppression in Sampled-Data Systems
277
1
Digital Redesign for Chaos Control
278
13
Summary
291
2
Engineering Feedback Control (III)
293
42
Occasional Proportional Feedback Control
293
4
Delayed Feedback Control
297
4
Methods from Mechanical Engineering
301
4
Dissipative Controller Design
301
2
Absorber as Controller
303
2
Stochastic Control Approaches
305
9
A Stochastic Control Method
306
3
Stochastic Modeling for Chaos Control
309
2
Probabilistic Control of Chaos
311
2
Chaos Control under a Statistical Criterion
313
1
Distortion Control via Harmonic Balance
314
9
Harmonic Balance Analysis
314
5
Predicting Chaos via Harmonic Balance
319
2
Distortion Control of Chaos
321
2
Filtering Applied to Chaos Control
323
5
Kalman Filter and Chaos
323
1
Controlling Chaos Using a Notch Filter
324
4
Entropy Reduction for Chaos Rejection
328
5
Summary
333
2
Adaptive Control of Chaos
335
74
Adaptive Control: An Example
336
2
Typical Adaptive Control Algorithms
338
6
Two Typical Adaptive Control Methods
338
4
Projection-Estimation and LMS Schemes
342
2
Chaos in Adaptive Control Systems
344
5
Complex Dynamics in MRAC and STAC Systems
345
4
Chaos in Other Adaptive Control Systems
349
1
An Example of Adaptive Control of Chaos
349
2
Gradient Based Adaptive Control
351
7
Examples of Gradient Based Control of Chaos
354
3
Gradient Model-Referenced Adaptive Control
357
1
Self-Tuning Adaptive Control of Chaos
358
13
Self-Tuning Control of Cardiac Chaos
359
5
Autoregressive Self-Tuning Feedback Control
364
7
The Lyapunov Function Approach
371
14
MRAC and Differential Inclusion Approach
372
4
Adaptive Control of Uncertain Chaotic Systems
376
9
Model Reconstruction Based Controls
385
18
Adaptive Control Based on Model Reconstruction
386
2
Adaptive Control Based on ARMA Models
388
5
A General Model Reconstruction Based Approach
393
10
Parametric Variation Based Controls
403
3
Summary
406
3
Intelligent Control of Chaos
409
74
Artificial Neural Networks
411
8
General Structure of Neural Networks
411
4
Functional Approximation by Neural Networks
415
4
Chaos in Neural Networks
419
6
Controlling Chaos in Neural Networks
425
6
Chaos Identification via Neural Networks
431
11
A General Setup for Chaos Identification
431
2
A Wiener-Type Model for Chaos Identification
433
9
Chaos Control by Neural Networks
442
7
Examples of Neural Network Based Chaos Control
442
5
Further Discussion
447
2
Fuzzy Control Systems
449
13
General Structure of Fuzzy Control Systems
451
5
Fuzzy Logic Control: Two Basic Approaches
456
6
Chaos in Fuzzy Control Systems
462
3
Controlling Chaos Using Fuzzy Logic
465
16
Controlling Chaos by Adaptive Fuzzy Method
465
10
A Combined Modeling and Control Approach
475
4
Some Related Developments
479
2
Summary
481
2
Chaos Control in Distributed Systems
483
54
Distributed Parameter Control Systems
484
2
Chaos in Spatiotemporal Systems
486
1
Controlling Spatiotemporal Chaos
487
11
Controlling Spatiotemporal Chaos in Plasma
489
4
Controlling Chaos in Isotropic Systems
493
5
Controlling Transport in Chaotic Lattices
498
4
Localized Control of Chaos
502
22
Local Controls of a Nonlinear Network Model
503
4
Controlling a Chain of Coupled Nonlinear Maps
507
4
Local Control of Coupled Logistic Networks
511
3
Parameter Variation versus Feedback Pinning
514
8
Local versus Global Controls
522
2
Decentralized Control of Chaos
524
4
Controlling Chaos in DAI Systems
528
6
Chaos in DAI Systems
529
2
Using Reward Policy to Control Chaos
531
3
Summary
534
3
Chaos Synchronization
537
82
What is Synchronization?
538
8
Synchronization as Result of Coupled Oscillations
538
5
Chaos Synchronization: A Drive-Response Setup
543
3
Synchronization Based on System Decomposition
546
11
Realizing Drive and Response by Decomposition
546
1
Synchronizing by Homogeneous Driving
547
4
Stability Analysis for Chaos Synchronization
551
6
Chaos Synchronization via Feedback
557
15
Synchronization of Identical Subsystems
557
1
Adaptive Synchronization
558
9
Chaos Synchronization with Observer
567
2
Two Simple Ways to Synchronize Chaos
569
3
Chaos Synchronization via System Inverse
572
3
More on Chaos Synchronization
575
20
Generalized Synchronization
576
1
Phase Synchronization
577
2
Synchronizing Higher-Dimensional and Spatiotemporal Chaos
579
6
Synchronization via the OLC Method
585
3
Synchronization Using Contraction Mappings
588
2
Stochastic Synchronization
590
2
Dead-Beat Chaos Synchronization
592
3
Chaos Control versus Chaos Synchronization
595
3
Synchronization and Communication
598
19
Communication Based on Chaos Synchronization
598
5
Robustness of Chaos Synchronization
603
3
Dead-Beat Synchronization for Communication
606
3
Implementation of Chaos Synchronization Based Communication
609
5
Chaotic Signal Encoding: A Biological Inspiration
614
3
Summary
617
2
More on Chaos Control
619
74
Controlling Bifurcation's
620
18
Bifurcations in Control Systems
621
7
Some Bifurcation Control Approaches
628
10
Controlling Multiple Limit Cycles
638
15
Graphical Hopf Bifurcation Theorem
639
3
Controlling the Birth of Multiple Limit Cycles
642
4
Controlling the Amplitudes of Limit Cycles
646
7
Chaos, Synchronization, and Disorder
653
4
Taming Spatiotemporal Chaos with Disorder
653
4
Disorder-Enhanced Synchronization
657
1
Pattern Formation, Self-Organization, and Chaos Control
657
17
Pattern Formation
659
4
Classification of Patterns
663
3
Pattern Formation and Control
666
8
Anticontrol of Chaos
674
17
Why Anticontrol of Chaos?
677
2
Toward Anticontrol of Chaos
679
12
Summary
691
2
Epilogue
693
2
References
695
50
Notation
745
4
Index
749