Optimal control and forecasting of complex dynamical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific
2006
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 198 S. Ill., graph. Darst. |
| ISBN: | 9812566600 |
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MARC
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| 245 | 1 | 0 | |a Optimal control and forecasting of complex dynamical systems |c Ilya Grigorenko |
| 264 | 1 | |a New Jersey |b World Scientific |c 2006 | |
| 300 | |a XIII, 198 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 4 | |a Differentiable dynamical systems | |
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Record in the Search Index
| _version_ | 1804137220063363072 |
|---|---|
| adam_text | Contents
Preface vii
1.
Analytical methods in control and optimization
1
1.1
Calculus of variations
..................... 1
1.1.1
The beginning: Fermat s variational principle
.... 2
1.1.2
The beautiful Brachistochrone Problem
...... 4
1.1.3
Euler-Lagrange equation
................ 6
1.1.4
A word about distance between two functions
.... 11
1.1.5
The Brachistochrone problem revisited
........ 12
1.1.6
Generalizations of the Euler-Lagrange equation
... 14
1.1.7
Transversality conditions
............... 16
1.1.8
Conditional
extrémům:
Lagrange
multipliers method
16
1.1.9
Mixed Optimal problem
................ 19
1.1.10
Approximate methods of solution-Ritz s method
... 20
1.2
Optimal control theory
..................... 21
1.2.1
Sensitivity analysis
................... 25
1.2.2
Null controllability
................... 26
1.2.3
Problems with constrained control
.......... 26
1.3
Summary
............................ 27
2.
Numerical optimization
29
2.1
The halting problem and No Free Lunch Theorem
..... 29
2.2
Global Optimization: searching for the deepest hole on a golf
field in the darkness using a cheap laser pointer
....... 30
2.2.1
Sensitivity to numerical errors
............. 33
2.3
Multiobjective optimization
.................. 34
2.3.1
Pareto front
....................... 35
2.3.2
The weighted-sum method
............... 37
2.4
Simplex method
........................ 38
2.5
Simulated annealing: crystallizing solutions
........ 42
2.6
Introduction to genetic algorithms
.............. 44
2.7
GA for a class of smooth (differentiable) functions
..... 49
2.8
Application of the GA to the eigenproblem
......... 57
2.8.1
The ground state problem in one and two dimensions
58
2.8.2
Extension of the QGA to quantum statistical problems
66
2.8.3
Formation of a Wigner molecule and its melting
69
2.9
Evolutionary gradient search and Lamarckianism
...... 74
2.10
Summary
............................ 76
3.
Chaos in complex systems
77
3.1 Lorenz attractor ........................ 80
3.2
Control of chaotic dynamics of the fractional
Lorenz
system
83
3.3
Summary
............................ 91
4.
Optimal control of quantum systems
93
4.1
Density matrix formalism
................... 95
4.2
Liouville equation for the reduced density matrix
...... 96
4.3
Modern variational approach to optimal control of quantum
systems
............................. 99
4.3.1
An alternative analytical theory
............ 100
4.4
An approximate analytical solution for the case of a two level
system
.............................. 105
4.5
Optimal control of a time averaged occupation of the excited
level in a two-level system
................... 109
4.5.1
Analytical solution for optimal control field
..... 114
4.5.2
Optimal control at a given time
............ 117
4.5.3
Estimation of the absolute bound for the control due
to decoherence
..................... 119
4.6
Optimal control of nanostructures: double quantum dot
. . 121
4.6.1
The optimal field for the control of the photon assisted
tunnelling between quantum dots
........... 124
4.7
Analytical theory for control of multi-photon transitions
. . 138
4.8
Summary
............................ 145
5.
Optimal control and quantum computing
147
Contents xiii
5.1
Robust two-qubit quantum registers
............. 147
5.2
Optimal design of universal two-qubit gates
......... 157
5.3
Entanglement of a pair of qubits
............... 166
5.4
Summary
............................ 168
6.
Forecasting of complex dynamical systems
171
6.1
Forecasting of financial markets
................ 171
6.2
Autoregressive
models
..................... 172
6.3
Chaos theory embedding dimensions
............. 174
6.4
Modelling of economic agents and
El Farol
bar problem
. 175
6.5
Forecasting of the solar activity
................ 176
6.6
Noise reduction and Wavelets
................. 177
6.7
Finance and random matrix theory
.............. 179
6.8
Neural Networks
........................ 180
6.9
Summary
............................ 181
Bibliography
183
Index
197
|
| adam_txt |
Contents
Preface vii
1.
Analytical methods in control and optimization
1
1.1
Calculus of variations
. 1
1.1.1
The beginning: Fermat's variational principle
. 2
1.1.2
The "beautiful" Brachistochrone Problem
. 4
1.1.3
Euler-Lagrange equation
. 6
1.1.4
A word about distance between two functions
. 11
1.1.5
The Brachistochrone problem revisited
. 12
1.1.6
Generalizations of the Euler-Lagrange equation
. 14
1.1.7
Transversality conditions
. 16
1.1.8
Conditional
extrémům:
Lagrange
multipliers method
16
1.1.9
Mixed Optimal problem
. 19
1.1.10
Approximate methods of solution-Ritz's method
. 20
1.2
Optimal control theory
. 21
1.2.1
Sensitivity analysis
. 25
1.2.2
Null controllability
. 26
1.2.3
Problems with constrained control
. 26
1.3
Summary
. 27
2.
Numerical optimization
29
2.1
The halting problem and No Free Lunch Theorem
. 29
2.2
Global Optimization: searching for the deepest hole on a golf
field in the darkness using a cheap laser pointer
. 30
2.2.1
Sensitivity to numerical errors
. 33
2.3
Multiobjective optimization
. 34
2.3.1
Pareto front
. 35
2.3.2
The weighted-sum method
. 37
2.4
Simplex method
. 38
2.5
Simulated annealing: "crystallizing" solutions
. 42
2.6
Introduction to genetic algorithms
. 44
2.7
GA for a class of smooth (differentiable) functions
. 49
2.8
Application of the GA to the eigenproblem
. 57
2.8.1
The ground state problem in one and two dimensions
58
2.8.2
Extension of the QGA to quantum statistical problems
66
2.8.3
Formation of a "Wigner molecule" and its "melting"
69
2.9
Evolutionary gradient search and Lamarckianism
. 74
2.10
Summary
. 76
3.
Chaos in complex systems
77
3.1 Lorenz attractor . 80
3.2
Control of chaotic dynamics of the fractional
Lorenz
system
83
3.3
Summary
. 91
4.
Optimal control of quantum systems
93
4.1
Density matrix formalism
. 95
4.2
Liouville equation for the reduced density matrix
. 96
4.3
Modern variational approach to optimal control of quantum
systems
. 99
4.3.1
An alternative analytical theory
. 100
4.4
An approximate analytical solution for the case of a two level
system
. 105
4.5
Optimal control of a time averaged occupation of the excited
level in a two-level system
. 109
4.5.1
Analytical solution for optimal control field
. 114
4.5.2
Optimal control at a given time
. 117
4.5.3
Estimation of the absolute bound for the control due
to decoherence
. 119
4.6
Optimal control of nanostructures: double quantum dot
. . 121
4.6.1
The optimal field for the control of the photon assisted
tunnelling between quantum dots
. 124
4.7
Analytical theory for control of multi-photon transitions
. . 138
4.8
Summary
. 145
5.
Optimal control and quantum computing
147
Contents xiii
5.1
Robust two-qubit quantum registers
. 147
5.2
Optimal design of universal two-qubit gates
. 157
5.3
Entanglement of a pair of qubits
. 166
5.4
Summary
. 168
6.
Forecasting of complex dynamical systems
171
6.1
Forecasting of financial markets
. 171
6.2
Autoregressive
models
. 172
6.3
Chaos theory embedding dimensions
. 174
6.4
Modelling of economic "agents" and
El Farol
bar problem
. 175
6.5
Forecasting of the solar activity
. 176
6.6
Noise reduction and Wavelets
. 177
6.7
Finance and random matrix theory
. 179
6.8
Neural Networks
. 180
6.9
Summary
. 181
Bibliography
183
Index
197 |
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| spelling | Grigorenko, Ilia A. 1974- Verfasser (DE-588)124430147 aut Optimal control and forecasting of complex dynamical systems Ilya Grigorenko New Jersey World Scientific 2006 XIII, 198 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Control theory Mathematical optimization Chaotic behavior in systems Differentiable dynamical systems Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016173502&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grigorenko, Ilia A. 1974- Optimal control and forecasting of complex dynamical systems Control theory Mathematical optimization Chaotic behavior in systems Differentiable dynamical systems |
| title | Optimal control and forecasting of complex dynamical systems |
| title_auth | Optimal control and forecasting of complex dynamical systems |
| title_exact_search | Optimal control and forecasting of complex dynamical systems |
| title_exact_search_txtP | Optimal control and forecasting of complex dynamical systems |
| title_full | Optimal control and forecasting of complex dynamical systems Ilya Grigorenko |
| title_fullStr | Optimal control and forecasting of complex dynamical systems Ilya Grigorenko |
| title_full_unstemmed | Optimal control and forecasting of complex dynamical systems Ilya Grigorenko |
| title_short | Optimal control and forecasting of complex dynamical systems |
| title_sort | optimal control and forecasting of complex dynamical systems |
| topic | Control theory Mathematical optimization Chaotic behavior in systems Differentiable dynamical systems |
| topic_facet | Control theory Mathematical optimization Chaotic behavior in systems Differentiable dynamical systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016173502&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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