Cybernetical Physics: From Control of Chaos to Quantum Control

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Springer, 30.06.2007 - 236 Seiten
In this book a number of ideas and results related to the ?eld of cybern- ical physics – the scienti?c area aimed at the study of physical systems by cybernetical means – are presented. Although some publications in physical journals related to control problems appeared long ago, formation of a se- rateself-sustainedareastartedaslateasinthe1990sduetotheexplosion-like developmentofresearchincontrolofchaos,quantumcontrol,andotherareas. The number of publications has reached several thousands by the end of the century and it continues to grow very rapidly. This book is, perhaps, the ?rst attempt to present a uni?ed exposition of the subject and methodology of cybernetical physics as well as solutions to some of its problems. A part of this book presents the limits of system transformation by means of control both for conservative and for dissipative systems based on Hamiltonian description of system dynamics. A survey of various control applications in physics is given: control of chaos, controlled synchronization, control of spatiotemporal systems, control ofmolecularandquantumsystems.Anapproachforbuildingmodelsofsystem dynamics based on control methods is discussed. The presented methods and results are illustrated by examples of new approaches to classical problems: Stephenson–Kapitsa pendulum, escape from a potential well, synchronization of coupled oscillators, control of chemical reaction with phase transition, c- trolled dissociation of molecules, controlled oscillations of complex crystalline lattices. Controlled pendulums appear in many parts of the book since p- dulum models can be thought of as the “atoms of nonlinear physics”.
 

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Inhalt

Introduction Physics and Cybernetics
1
12 Control of chaos
2
13 Control of molecules
4
14 Physics and information
5
142 Physics from information
7
15 Physics animal and machine
10
16 Types of control
11
17 What is the use of control in physics?
13
623 Delayed coordinates and Poincaré map
110
63 Models of controlled systems and control goals
111
Continuoustime control
113
642 Linearization of Poincaré map OGY method
116
643 Delayed feedback Pyragas method
119
644 Linear and nonlinear control
121
645 Adaptive control
126
65 Discretetime control
127

172 Opinion of cyberneticians
15
Subject and Methodology of Cybernetical Physics
17
22 Control goals
21
23 Control algorithms
26
24 Methodology
27
241 Gradient method
28
242 Speedgradient method
29
243 Feedback linearization
32
Laws of cybernetical physics
34
Control of Conservative Systems
36
Controlled pendulum
41
33 The swinging small control property
42
34 Control of first integrals
43
35 Control of generalized Hamiltonian systems
46
Control of Dissipative Systems
49
411 Excitability index
50
412 Properties of excitability index
51
413 Case of EulerLagrange systems
54
Excitation of the dumped pendulum
55
42 Feedback resonance
57
43 Excitability index of pendulum systems
60
Controlled Synchronization
67
511 Evolution of the synchronization concept
68
512 Synchronization of processes
69
513 Examples
70
514 Synchronization of systems
72
515 Discussion
76
52 Controlled synchronization design
78
521 Synchronization and convergence
79
522 Synchronization and stabilization
80
523 Synchronization and observers
82
524 Synchronization of affine nonlinear systems
83
525 PecoraCarroll scheme
84
526 Synchronization and speedgradient
86
53 Adaptive synchronization
87
533 Conditions for control goal achievement
89
534 Synchronization and adaptive observers
92
Information transmission using chaotic Chua system
95
54 Synchronization of two coupled pendulums
98
Control of Chaos
105
62 Notion of chaos
106
622 Criteria of chaos
109
66 Generation of chaos chaotization
128
67 Time and energy needed for control of chaos
129
68 Applications in physics
133
682 Control of lasers
134
69 Other problems
136
Control of Interconnected and Distributed Systems
137
72 Control of energy in sinGordon and FrenkelKontorova models
139
73 Control of wave motion in the chain of pendulums
142
732 Problem statement and control algorithm design
143
733 Simulation results
144
74 Control of oscillations in a complex crystalline lattice
148
741 Modeling interaction of acoustic and optical modes
149
742 Control law design
151
743 Nonfeedback control
153
75 Control of chaos in distributed systems
155
752 Delayed systems
157
753 Chaotic mixing
158
Control of Molecular and Quantum Systems
160
82 Controlled dissociation of diatomic molecules classical design
164
822 Simulation results classical model
166
83 Control of finitelevel quantum systems
168
Control Algorithms and Dynamics of Physical Systems
173
92 Examples of speedgradient laws of dynamics
174
93 Speedgradient entropy maximization
176
94 Onsager relations
179
Dynamics and the purpose
181
Examples
183
102 Escape from a potential well and lossless communications
188
103 Feedback spectroscopy
192
104 Control of chemical reaction with phase transition
193
1042 Adaptive control algorithm
194
1043 Simulation results
196
105 Energylike control of predatorprey system
199
106 Control of noiseinduced transition
202
1061 The system model and problem statement
203
1062 Control algorithm design
205
1063 Control system analysis
206
1064 Discussion
210
Conclusions Looking into the Future
212
References
217
Index
239
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Seite 1 - Cybernetics [44] was published bringing together contemporary ideas about control processes and establishing the famous definition of cybernetics as the science of control and communication in the animal and the machine.

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