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Tables of Contents for Controlling Chaos and Bifurcations in Engineering Systems
Chapter/Section Title
Page #
Page Count
Foreword
v
Preface
vii
Reconstructing Input-Output Dynamics from Time Series
1
22
A. I. Mees
Introduction
2
1
Embeddings for Systems with Inputs
3
3
Selecting Modeling Variables
6
3
Model Types
9
5
An Approach to Reconstructing Dynamics of Input-Output Systems
14
1
Examples
15
8
Black and Grey-Box Modeling of Nonlinear Systems: Identification and Analysis From Time Series
23
22
L. A. Aguirre
Introduction
24
1
Modeling of Nonlinear Dynamics: Representations and Techniques
24
4
NARX Polynomial Models
28
3
Static Nonlinearities in NARX Models
31
1
Identification of a Buck Converter
32
4
Model-Based Analysis of Breathing Patterns
36
4
Final Remarks
40
5
Design and Implementation of Chaos Control Systems
45
26
M. J. Ogorzalek
Why Chaos Control
46
5
Conditions for Implementation of Chaos Controllers
51
1
Short Description of the OGY Technique
52
2
Implementation Problems for the OGY Method
54
5
Brief Review of the OPF Controller
59
3
Improved Chaos Controller for Autonomous Circuits
62
1
Working Laboratory Chaos Control Systems
63
2
Conclusions
65
6
Chaos in Mechanical Systems and Its Control
71
18
T. Kapitaniak
J. Brindley
K. Czolczynski
Introduction
72
1
Methods of Chaos Control
72
3
Nonlinearities in Mechanical Systems
75
3
Control Through Operating Conditions
78
5
Control by System Design
83
2
Discussion
85
4
Utilizing Chaos in Control System Design
89
18
T. L. Vincent
Introduction
90
2
Chaotic Control Algorithm
92
3
Inverted Pendulum
95
8
Discussion
103
4
Control and Synchronization of Spatiotemporal Chaos
107
24
J.-Q. Fang
M. K. Ali
Introduction
108
1
SESs Modeled by PDEs
108
7
SESs Modeled by Coupled ODEs
115
4
SESs Modeled by Coupled Map Lattices
119
4
Some Characteristic Quantitates and Mechanisms
123
2
New Research Outlook
125
1
Summary
126
5
Chaotic Vibration of the Wave Equation by Nonlinear Feedback Boundary Control
131
24
G. Chen, S.-B. Hsu
J. Zhou
Introduction
132
2
Chaos Induced by Boundary Feedback
134
7
Feedback of Polynomial Type at the Right Endpoint
141
9
Concluding Remarks
150
5
Sensitivity to Initial Conditions of Chaos in Electronics
155
24
G. Q. Zhong
Z. F. Liu
K. S. Tang
K. F. Man
S. Kwong
Introduction
156
1
Phase Model of PLL
157
2
PLL with Nonlinear Control
159
5
Chaotic Characteristics of the Controlled PLL
164
3
Synchronization with PLLs
167
9
Conclusion
176
3
Frequency Domain Methods for Chaos Control
179
26
M. Basso
R. Genesio
L. Giovanardi
A. Tesi
Introduction
180
2
System Setup
182
3
Existence of Periodic Solutions
185
2
Stability of Periodic Solutions
187
8
Application to Chaos Control
195
5
Conclusions
200
5
Controlling Limit Cycles and Bifurcations
205
28
G. Calandrini
E. Paolini
J. L. Moiola
G. Chen
Introduction
206
2
Harmonic Balance and Curvature Coefficients
208
6
Normal Forms and Limit Cycles
214
3
Controlling the Multiplicity of Limit Cycles
217
2
Two Illustrative Examples
219
8
Conclusions
227
6
Theory and Experiments on Nonlinear Time-Delayed Feedback Systems with Application to Chaos Control
233
22
P. Celka
Introduction
234
1
Delay-Differential Equations as Models
234
4
From Continuous to Discrete-Time Models
238
4
Control of DDE Using Delayed Self-Feedback
242
7
Conclusions
249
6
Time Delayed Feedback Control of Chaos
255
20
X. Yu
Y. Tian
G. Chen
Introduction
256
1
Chaos Control with Linear TDFC
257
3
Chaos Control by Sliding Mode Based TDFC
260
3
TDFC Design Based on an Optimal Principle
263
4
Estimation of Delay Time τ
267
1
Simulation Studies
268
4
Conclusions
272
3
Impulsive Control and Synchronization of Chaos
275
24
J. A. K. Suykens
T. Yang
J. Vandewalle
L. O. Chua
Introduction
276
1
Basic Theory of Impulsive Differential Equations
277
4
Impulsive Synchronization of Lur'e Systems
281
6
Impulsive Control to Periodic Motions
287
5
Experimental Confirmation, Secure Communications, and (CD)2MA
292
1
Conclusions
292
7
Control and Anticontrol of Bifurcations with Application to Active Control of Rayleigh-Benard Convection
299
26
H. O. Wang
D. S. Chen
Introduction
300
2
Anticontrol of Bifurcations
302
8
Amplitude Control of Bifurcations
310
2
Bifurcation Control of Rayleigh-Benard Convection
312
8
Conclusions
320
5
Delay Feedback Control of Cardiac Activity Models
325
22
M. E. Brandt
G. Chen
Introduction and Background
326
2
TDF Control of a Quadratic Map Model of Cardiac Chaos
328
4
TDF Control of a Circle-Map Cardiac Model
332
7
Linear TDF Control of a Cardiac Conduction Model
339
4
Discussion
343
4
Bifurcation Stabilization with Applications in Jet Engine Control
347
22
G. Gu
A. Sparks
Introduction
348
1
Local Stability and Stabilization for Hopf Bifurcations
349
4
Multi-Mode Moore-Greitzer Model
353
6
Rotating Stall Control
359
4
Simulation Results and Discussions
363
6
Bifurcations of Control Systems in Normal Form
369
22
W. Kang
Introduction
370
1
Problem Formulation
371
3
Normal Forms and Invariants
374
4
Bifurcations of System with Quadratic Degeneracy
378
4
Bifurcations of System with Cubic Degeneracy
382
2
Application Example of Bifurcation Control
384
2
Conclusions
386
5
Controlling Bifurcations in Nonsmooth Dynamical Systems
391
26
M. di Bernardo
G. Chen
Introduction
392
1
Some Typical Dynamical Phenomena in PWS Systems
393
4
Two Examples: Chua's Circuit and the Buck Converter
397
4
Control of Border-Collision Bifurcations
401
3
Feedback Control of PWS Chaotic Systems
404
6
Other Control Techniques
410
2
Conclusions
412
5
Adaptive Observer--Based Synchronization
417
22
A. L. Fradkov
H. Nijmeijer
A. Y. Pogromsky
Introduction
418
1
General Definition of Synchronization
419
2
Adaptive Observers
421
4
Adaptive Synchronization of Lur'e Systems
425
4
Signal Transmission and Reconstruction
429
3
Conclusions
432
7
Discrete-Time Observers and Synchronization
439
18
H. J. C. Huijberts
H. Nijmeijer
A. Y. Pogromsky
Introduction
440
1
Preliminaries and Problem Statement
441
1
Systems in Lur'e Form
442
3
Transformation into Lur'e Form
445
3
Transformation into Extended Lur'e Form
448
3
Observers for Perturbed Linear Systems
451
2
Conclusions
453
4
Separating a Chaotic Signal from Noise and Applications
457
20
H. Dedieu
T. Schimming
M. Hasler
Introduction
458
1
Definition of the Problem
459
1
Optimal Solution without Dynamic Constraint on the Estimator
460
3
Optimal Solution with Dynamic Constraint on the Estimator
463
2
Practical Algorithms for Noise Cleaning: Deterministic Approach
465
2
Practical Algorithms for Noise Cleaning: Probabilistic Approach
467
4
Communication Applications
471
3
Conclusions
474
3
Digital Communications Using Chaos
477
24
M. P. Kennedy
G. Kolumban
Motivation
478
1
What is Chaos?
479
1
Potential Benefits of Chaotic Basis Functions in Digital Communications
479
1
Digital Communications Using Chaos
480
4
Survey of Noncoherent Chaotic Communication Schemes
484
12
Summary
496
1
Open Problems and Expected Developments
497
4
Synchronization in Arrays of Coupled Chaotic Circuits and Systems: Theory and Applications
501
28
C. W. Wu
Introduction
502
1
Notation and Terminology
502
1
Synchronization of Chaotic Circuits and Systems
503
3
Static Coupling
506
5
Dynamic Coupling
511
5
Discrete-Time Systems
516
3
Lyapunov Exponents Approach
519
3
Dynamics at Synchronization
522
1
Synchronization of Clusters
523
1
Applications to Graph Coloring
524
5
Chaos in Phase Systems: Generation and Synchronization
529
30
V. D. Shalfeev
V. V. Matrosov
M. V. Korzinova
Introduction
530
1
A PLL System as a Generator of Chaotic Oscillations
531
6
Chaotic Regimes in an Ensemble of Two Coupled PLLs
537
6
Synchronization of Chaotic Oscillations
543
10
Application of Chaotic PLLs to Transmission of Information
553
1
Conclusion
554
5
Chaos and Bifurcations in Feedback Control Systems
559
22
J. Alvarez
F. Verduzco
Introduction
560
1
Prediction of Chaos
560
3
Linear Plants with Classical Controllers
563
6
PD-Controlled Robot Manipulators
569
9
Conclusions
578
3
Chaos and Bifurcations in Coupled Networks and Their Control
581
22
T. Ueta
G. Chen
Introduction
582
2
Some Simple Equilibria in the System
584
2
Periodic Solutions and Chaos
586
10
Controlling to Unstable Periodic Orbits
596
3
Concluding Remarks
599
4
Return Map Modulation in Nonautonomous Relaxation Oscillator
603
22
T. Saito
H. Torikai
Introduction
604
1
Unit Shape Function
605
2
Integrate-and-Fire Model with Three Inputs
607
2
Basic Return Map by the First Prime Input
609
4
Role of the Second Base Input
613
3
Role of the Threshold Input
616
4
Conclusions
620
5
Controlling Chaos in Discrete-Time Computational Ecosystems
625
20
T. Ushio
T. Imamori
T. Yamasaki
Introduction
626
1
The Discrete Time Hogg-Huberman Model
627
2
Analysis of Fixed Points
629
1
Net Bias and Transient Behavior
630
6
Application to a Routing Problem
636
5
Conclusions
641
4
Index
645