Cybernetical physics: from control of chaos to quantum control
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer Berlin
2007
|
| Edition: | 1. Ed. |
| Series: | Understanding Complex Systems
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 241 S. graph. Darst. |
| ISBN: | 9783540462750 3540462759 |
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Contents
1 Introduction: Physics and Cybernetics 1
1.1 Looking into the past 1
1.2 Control of chaos 2
1.3 Control of molecules 4
1.4 Physics and information 5
1.4.1 Information is physical 5
1.4.2 Physics from information 7
1.5 Physics, animal, and machine 10
1.6 Types of control 11
1.7 What is the use of control in physics? 13
1.7.1 Opinion of physicists 13
1.7.2 Opinion of cyberneticians 15
2 Subject and Methodology of Cybernetical Physics 17
2.1 Models of controlled systems 17
2.2 Control goals 21
2.3 Control algorithms 26
2.4 Methodology 27
2.4.1 Gradient method 28
2.4.2 Speed gradient method 29
2.4.3 Feedback linearization 32
2.5 Results: Laws of cybernetical physics 34
3 Control of Conservative Systems 37
3.1 Control of energy for Hamiltonian systems 37
3.2 Example: Controlled pendulum 41
3.3 The swinging (small control) property 42
3.4 Control of first integrals 43
3.5 Control of generalized Hamiltonian systems 46
X Contents
4 Control of Dissipative Systems 49
4.1 Excitability analysis of dissipative systems 49
4.1.1 Excitability index 50
4.1.2 Properties of excitability index 51
4.1.3 Case of Euler Lagrange systems 54
4.1.4 Example: Excitation of the dumped pendulum 55
4.1.5 Example: Excitation of the Duffing system 55
4.2 Feedback resonance 57
4.3 Excitability index of pendulum systems 60
5 Controlled Synchronization 67
5.1 Definitions of synchronization 67
5.1.1 Evolution of the synchronization concept 68
5.1.2 Synchronization of processes 69
5.1.3 Examples 70
5.1.4 Synchronization of systems 72
5.1.5 Discussion 76
5.2 Controlled synchronization design 78
5.2.1 Synchronization and convergence 79
5.2.2 Synchronization and stabilization 80
5.2.3 Synchronization and observers 82
5.2.4 Synchronization of affine nonlinear systems 83
5.2.5 Pecora Carroll scheme 84
5.2.6 Synchronization and speed gradient 86
5.3 Adaptive synchronization 87
5.3.1 Problem formulation 87
5.3.2 Adaptive synchronization of two subsystems 87
5.3.3 Conditions for control goal achievement 89
5.3.4 Synchronization and adaptive observers 92
5.3.5 Example: Information transmission using chaotic
Chua system 95
5.4 Synchronization of two coupled pendulums 98
6 Control of Chaos 105
6.1 Introduction 105
6.2 Notion of chaos 106
6.2.1 Definitions of chaos 106
6.2.2 Criteria of chaos 109
6.2.3 Delayed coordinates and Poincare map 110
6.3 Models of controlled systems and control goals Ill
6.4 Methods of controlling chaos: Continuous time control 113
6.4.1 Feedforward control by periodic signal 113
6.4.2 Linearization of Poincare map (OGY method) 116
6.4.3 Delayed feedback (Pyragas method) 119
6.4.4 Linear and nonlinear control 121
Contents XI
6.4.5 Adaptive control 126
6.5 Discrete time control 127
6.6 Generation of chaos (chaotization) 128
6.7 Time and energy needed for control of chaos 129
6.8 Applications in physics 133
6.8.1 Control of turbulence 133
6.8.2 Control of lasers 134
6.8.3 Control of chaos in plasma 134
6.9 Other problems 136
7 Control of Interconnected and Distributed Systems 137
7.1 Models of controlled spatiotemporal systems 137
7.2 Control of energy in sin Gordon
and Frenkel Kontorova models 139
7.3 Control of wave motion in the chain of pendulums 142
7.3.1 Modeling the chain of the pendulums 142
7.3.2 Problem statement and control algorithm design 143
7.3.3 Simulation results 144
7.4 Control of oscillations in a complex crystalline lattice 148
7.4.1 Modeling interaction of acoustic and optical modes . 149
7.4.2 Control law design 151
7.4.3 Nonfeedback control 153
7.5 Control of chaos in distributed systems 155
7.5.1 Spatiotemporal systems 155
7.5.2 Delayed systems 157
7.5.3 Chaotic mixing 158
8 Control of Molecular and Quantum Systems 161
8.1 Laser control of molecular dynamics 161
8.2 Controlled dissociation of diatomic molecules (classical design) 164
8.2.1 Control algorithm design 164
8.2.2 Simulation results (classical model) 166
8.2.3 Comparison of classical and quantum simulations 166
8.3 Control of finite level quantum systems 168
9 Control Algorithms and Dynamics of Physical Systems . 173
9.1 Integral and differential variational principles 173
9.2 Examples of speed gradient laws of dynamics 174
9.3 Speed gradient entropy maximization 176
9.4 Onsager relations 179
9.5 Discussion: Dynamics and the purpose 181
XII Contents
10 Examples 183
10.1 Controlled Stephenson Kapitsa pendulum 183
10.2 Escape from a potential well and lossless communications 188
10.3 Feedback spectroscopy 192
10.4 Control of chemical reaction with phase transition 193
10.4.1 Problem statement 193
10.4.2 Adaptive control algorithm 194
10.4.3 Simulation results 196
10.5 Energy like control of predator prey system 199
10.6 Control of noise induced transition 202
10.6.1 The system model and problem statement 203
10.6.2 Control algorithm design 205
10.6.3 Control system analysis 206
10.6.4 Discussion 210
11 Conclusions: Looking into the Future 213
References 217
Index 239 |
| adam_txt |
Contents
1 Introduction: Physics and Cybernetics 1
1.1 Looking into the past 1
1.2 Control of chaos 2
1.3 Control of molecules 4
1.4 Physics and information 5
1.4.1 Information is physical 5
1.4.2 Physics from information 7
1.5 Physics, animal, and machine 10
1.6 Types of control 11
1.7 What is the use of control in physics? 13
1.7.1 Opinion of physicists 13
1.7.2 Opinion of cyberneticians 15
2 Subject and Methodology of Cybernetical Physics 17
2.1 Models of controlled systems 17
2.2 Control goals 21
2.3 Control algorithms 26
2.4 Methodology 27
2.4.1 Gradient method 28
2.4.2 Speed gradient method 29
2.4.3 Feedback linearization 32
2.5 Results: Laws of cybernetical physics 34
3 Control of Conservative Systems 37
3.1 Control of energy for Hamiltonian systems 37
3.2 Example: Controlled pendulum 41
3.3 The swinging (small control) property 42
3.4 Control of first integrals 43
3.5 Control of generalized Hamiltonian systems 46
X Contents
4 Control of Dissipative Systems 49
4.1 Excitability analysis of dissipative systems 49
4.1.1 Excitability index 50
4.1.2 Properties of excitability index 51
4.1.3 Case of Euler Lagrange systems 54
4.1.4 Example: Excitation of the dumped pendulum 55
4.1.5 Example: Excitation of the Duffing system 55
4.2 Feedback resonance 57
4.3 Excitability index of pendulum systems 60
5 Controlled Synchronization 67
5.1 Definitions of synchronization 67
5.1.1 Evolution of the synchronization concept 68
5.1.2 Synchronization of processes 69
5.1.3 Examples 70
5.1.4 Synchronization of systems 72
5.1.5 Discussion 76
5.2 Controlled synchronization design 78
5.2.1 Synchronization and convergence 79
5.2.2 Synchronization and stabilization 80
5.2.3 Synchronization and observers 82
5.2.4 Synchronization of affine nonlinear systems 83
5.2.5 Pecora Carroll scheme 84
5.2.6 Synchronization and speed gradient 86
5.3 Adaptive synchronization 87
5.3.1 Problem formulation 87
5.3.2 Adaptive synchronization of two subsystems 87
5.3.3 Conditions for control goal achievement 89
5.3.4 Synchronization and adaptive observers 92
5.3.5 Example: Information transmission using chaotic
Chua system 95
5.4 Synchronization of two coupled pendulums 98
6 Control of Chaos 105
6.1 Introduction 105
6.2 Notion of chaos 106
6.2.1 Definitions of chaos 106
6.2.2 Criteria of chaos 109
6.2.3 Delayed coordinates and Poincare map 110
6.3 Models of controlled systems and control goals Ill
6.4 Methods of controlling chaos: Continuous time control 113
6.4.1 Feedforward control by periodic signal 113
6.4.2 Linearization of Poincare map (OGY method) 116
6.4.3 Delayed feedback (Pyragas method) 119
6.4.4 Linear and nonlinear control 121
Contents XI
6.4.5 Adaptive control 126
6.5 Discrete time control 127
6.6 Generation of chaos (chaotization) 128
6.7 Time and energy needed for control of chaos 129
6.8 Applications in physics 133
6.8.1 Control of turbulence 133
6.8.2 Control of lasers 134
6.8.3 Control of chaos in plasma 134
6.9 Other problems 136
7 Control of Interconnected and Distributed Systems 137
7.1 Models of controlled spatiotemporal systems 137
7.2 Control of energy in sin Gordon
and Frenkel Kontorova models 139
7.3 Control of wave motion in the chain of pendulums 142
7.3.1 Modeling the chain of the pendulums 142
7.3.2 Problem statement and control algorithm design 143
7.3.3 Simulation results 144
7.4 Control of oscillations in a complex crystalline lattice 148
7.4.1 Modeling interaction of acoustic and optical modes . 149
7.4.2 Control law design 151
7.4.3 Nonfeedback control 153
7.5 Control of chaos in distributed systems 155
7.5.1 Spatiotemporal systems 155
7.5.2 Delayed systems 157
7.5.3 Chaotic mixing 158
8 Control of Molecular and Quantum Systems 161
8.1 Laser control of molecular dynamics 161
8.2 Controlled dissociation of diatomic molecules (classical design) 164
8.2.1 Control algorithm design 164
8.2.2 Simulation results (classical model) 166
8.2.3 Comparison of classical and quantum simulations 166
8.3 Control of finite level quantum systems 168
9 Control Algorithms and Dynamics of Physical Systems . 173
9.1 Integral and differential variational principles 173
9.2 Examples of speed gradient laws of dynamics 174
9.3 Speed gradient entropy maximization 176
9.4 Onsager relations 179
9.5 Discussion: Dynamics and the purpose 181
XII Contents
10 Examples 183
10.1 Controlled Stephenson Kapitsa pendulum 183
10.2 Escape from a potential well and lossless communications 188
10.3 Feedback spectroscopy 192
10.4 Control of chemical reaction with phase transition 193
10.4.1 Problem statement 193
10.4.2 Adaptive control algorithm 194
10.4.3 Simulation results 196
10.5 Energy like control of predator prey system 199
10.6 Control of noise induced transition 202
10.6.1 The system model and problem statement 203
10.6.2 Control algorithm design 205
10.6.3 Control system analysis 206
10.6.4 Discussion 210
11 Conclusions: Looking into the Future 213
References 217
Index 239 |
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| spelling | Fradkov, Aleksandr L. Verfasser aut Cybernetical physics from control of chaos to quantum control A. Fradkov 1. Ed. Berlin Springer Berlin 2007 XII, 241 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Understanding Complex Systems Commande non linéaire Nonlinear control theory Physikalisches System (DE-588)4174610-7 gnd rswk-swf Kybernetik (DE-588)4033888-5 gnd rswk-swf Physikalisches System (DE-588)4174610-7 s Kybernetik (DE-588)4033888-5 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2857286&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015620146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fradkov, Aleksandr L. Cybernetical physics from control of chaos to quantum control Commande non linéaire Nonlinear control theory Physikalisches System (DE-588)4174610-7 gnd Kybernetik (DE-588)4033888-5 gnd |
| subject_GND | (DE-588)4174610-7 (DE-588)4033888-5 |
| title | Cybernetical physics from control of chaos to quantum control |
| title_auth | Cybernetical physics from control of chaos to quantum control |
| title_exact_search | Cybernetical physics from control of chaos to quantum control |
| title_exact_search_txtP | Cybernetical physics from control of chaos to quantum control |
| title_full | Cybernetical physics from control of chaos to quantum control A. Fradkov |
| title_fullStr | Cybernetical physics from control of chaos to quantum control A. Fradkov |
| title_full_unstemmed | Cybernetical physics from control of chaos to quantum control A. Fradkov |
| title_short | Cybernetical physics |
| title_sort | cybernetical physics from control of chaos to quantum control |
| title_sub | from control of chaos to quantum control |
| topic | Commande non linéaire Nonlinear control theory Physikalisches System (DE-588)4174610-7 gnd Kybernetik (DE-588)4033888-5 gnd |
| topic_facet | Commande non linéaire Nonlinear control theory Physikalisches System Kybernetik |
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