Mathematical theory of adaptive control:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2006
|
| Schriftenreihe: | Interdisciplinary mathematical sciences
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 473 S. |
| ISBN: | 9812563717 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical theory of adaptive control |c Vladimir G. Sragovich |
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| 650 | 4 | |a Control theory |x Mathematical models | |
| 650 | 4 | |a Adaptive control systems | |
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Datensatz im Suchindex
| _version_ | 1804137220137811968 |
|---|---|
| adam_text | CONTENTS
Preface
vii
Editor s Note
xi
1.
Basic
Notions and Definitions
1
1.1.
Random Processes and Systems of Probability Distributions
.... 1
1.2.
Controlled Random Processes
..................... 5
1.3.
Definition of Adaptive Control
.................... 19
1.4.
Learning Systems
............................ 25
1.5.
Bayesian Approach on a Finite Interval
................ 29
2.
Real-Valued HPIV with Finite Number of Controls:
Automaton Approach
33
2.1.
Formulation of the Problem
...................... 33
2.2.
Optimal Properties of Finite Automata
................ 36
2.3.
Automata with Increasing Memory
.................. 49
2.4.
¿ω
-Automata
and Their Modifications
................ 55
2.5.
Automata with Formed Structure
................... 68
2.6.
Asymptotic Optimality of Automata with Variable Structure
... 72
3.
Stochastic Approximation
77
3.1.
Formulation of the Problem
...................... 77
3.2.
Convergence Conditions of Stochastic Approximation
Procedures
................................ 81
3.3.
Survey of Asymptotic Properties of Stochastic Approximation
Methods for HPIV
........................... 86
3.4.
Calculation of the Conditional
Extrémům
.............. 89
4. Minimax
Adaptive Control
97
4.1.
Games with Consistent Interests
................... 97
4.2.
Some Remarks on Minimax Control of Vector HPIV
........ 102
4.3.
Recurrent Procedure of Searching Equilibrium Strategies in a
Multi-person Game
........................... 104
4.4.
Games of Automata
.......................... 108
5.
Controlled Finite Homogeneous Markov Chains
123
5.1.
Preliminary Remarks
.......................... 123
5.2.
Structure of Finite Homogeneous Controlled Markov Chains
.... 125
5.3.
Unconditional Optimal Adaptive Control for Finite
Markov Chains
............................. 133
Contents
5.4. The First
Control Algorithm for a Class of Markov Chains
{identificationat)
............................ 136
5.5.
The Second Control Algorithm for a Class of Markov Chains
{automata)
............................... 139
5.6.
The Third Control Algorithm for a Class of Markov Chains
{stochastic approximation)
....................... 142
5.7.
Adaptive Optimization with Constraints on Markov Chains
.... 154
5.8.
Minimax Adaptive Problems on Finite Markov Chains
....... 161
5.9.
Controlled Graphs with Rewards
................... 167
Control of Partially Observable Markov Chains and
Regenerative Processes
173
6.1.
Preliminary Remarks
.......................... 173
6.2.
Control of Conditional Markov Chains
................ 174
6.3.
Optimal Adaptive Control of Partially Observable Markov Chains
and Graphs
............................... 181
6.4.
Control of Regenerative Processes
................... 184
6.5.
Structure of
ε
-optimal Strategies for Controlled
Regenerative Processes
......................... 186
6.6.
Adaptive Strategies for Controlled Regenerative Processes
..... 196
Control of Markov Processes with Discrete Time
and Semi-Markov Processes
203
7.1.
Preliminary Results
........................... 203
7.2.
Optimal Automaton Control for Markov Processes with A Compact
State Space and A Finite Control Set
................. 211
7.3.
Searching Optimal Strategies for Ergodic Markov Processes with
Compact Spaces of States and Controls
............... 215
7.4.
Control of Finite Semi-Markov Processes
............... 221
7.5.
Control of Countably Valued Semi-Markov Processes
........ 225
7.6.
Optimal Control of Special Classes of Markov Processes
with Discrete Time
........................... 237
Control of Stationary Processes
251
8.1.
Formulation of the Problem
...................... 251
8.2.
Some Properties of Stationary Processes
............... 252
8.3.
Auxiliary Results for CSP
....................... 254
8.4.
Adaptive Strategies for CSP
...................... 262
Finite-Converging Procedures for Control Problems
with Inequalities
267
9.1.
Formulation of the Problem
...................... 267
9.2.
Finite-converging Procedures of Solving A Countable System
of Inequalities
.............................. 269
9.3.
Sufficient Conditions for Existence of FCP
.............. 273
Contents xv
9.4.
Stabilization of Solutions of Linear Difference
Equations: Part I
............................276
9.5.
Stabilization of Solutions of Linear Difference
Equations: Part II
...........................281
10.
Control of Linear Difference Equations
287
10.1.
Auxiliary Results
........................... 287
10.2.
Control of Homogeneous Equations Xt+i
= Axt +
Вщ
....... 297
10.3.
Optimal Tracking Problem for ARMAX
.............. 302
10.4.
Optimal Tracking and Consistency of Estimates for ARMAX
. . . 310
10.5.
Adaptive Modal Control
....................... 320
10.6.
On Strong Consistency of
LSE
and SGE of Parameters
...... 328
10.7.
Linear-Quadratic Problem (LQP)
.................. 339
10.8.
LQP for ARMAX-type Equations
.................. 352
11.
Control of Ordinary Differential Equations
359
11.1.
Preliminary Results
.......................... 359
11.2.
Control of Homogeneous Equations
................. 365
11.3.
Control with A Model Reference
................... 370
11.4.
Steepest Descent Method
....................... 381
11.5.
Stabilization of Solutions of Minimum Phase Equations
...... 387
11.6.
Stabilization of Minimum Phase Equations
with Nonlinearities
.......................... 395
11.7.
Stabilization of Linear Minimum Phase Equations
in Hubert Space
............................ 397
11.8.
Control of Stabilizable Equations
.................. 404
11.9.
Two Special Problems of Adaptive Control
............. 413
12.
Control of Stochastic Differential Equations
421
12.1.
Preliminary Results
..........................421
12.2.
Stabilization of Solutions of Minimum Phase
Ito
Equations
.... 430
12.3.
Identification Methods for
Ito
Equations
..............439
12.4.
LQP for Stochastic
Ito
Equations
..................441
Comments and Supplements
445
General References
459
Special References
461
Additional References
469
Index
471
|
| adam_txt |
CONTENTS
Preface
vii
Editor's Note
xi
1.
Basic
Notions and Definitions
1
1.1.
Random Processes and Systems of Probability Distributions
. 1
1.2.
Controlled Random Processes
. 5
1.3.
Definition of Adaptive Control
. 19
1.4.
Learning Systems
. 25
1.5.
Bayesian Approach on a Finite Interval
. 29
2.
Real-Valued HPIV with Finite Number of Controls:
Automaton Approach
33
2.1.
Formulation of the Problem
. 33
2.2.
Optimal Properties of Finite Automata
. 36
2.3.
Automata with Increasing Memory
. 49
2.4.
¿ω
-Automata
and Their Modifications
. 55
2.5.
Automata with Formed Structure
. 68
2.6.
Asymptotic Optimality of Automata with Variable Structure
. 72
3.
Stochastic Approximation
77
3.1.
Formulation of the Problem
. 77
3.2.
Convergence Conditions of Stochastic Approximation
Procedures
. 81
3.3.
Survey of Asymptotic Properties of Stochastic Approximation
Methods for HPIV
. 86
3.4.
Calculation of the Conditional
Extrémům
. 89
4. Minimax
Adaptive Control
97
4.1.
Games with Consistent Interests
. 97
4.2.
Some Remarks on Minimax Control of Vector HPIV
. 102
4.3.
Recurrent Procedure of Searching Equilibrium Strategies in a
Multi-person Game
. 104
4.4.
Games of Automata
. 108
5.
Controlled Finite Homogeneous Markov Chains
123
5.1.
Preliminary Remarks
. 123
5.2.
Structure of Finite Homogeneous Controlled Markov Chains
. 125
5.3.
Unconditional Optimal Adaptive Control for Finite
Markov Chains
. 133
Contents
5.4. The First
Control Algorithm for a Class of Markov Chains
{identificationat)
. 136
5.5.
The Second Control Algorithm for a Class of Markov Chains
{automata)
. 139
5.6.
The Third Control Algorithm for a Class of Markov Chains
{stochastic approximation)
. 142
5.7.
Adaptive Optimization with Constraints on Markov Chains
. 154
5.8.
Minimax Adaptive Problems on Finite Markov Chains
. 161
5.9.
Controlled Graphs with Rewards
. 167
Control of Partially Observable Markov Chains and
Regenerative Processes
173
6.1.
Preliminary Remarks
. 173
6.2.
Control of Conditional Markov Chains
. 174
6.3.
Optimal Adaptive Control of Partially Observable Markov Chains
and Graphs
. 181
6.4.
Control of Regenerative Processes
. 184
6.5.
Structure of
ε
-optimal Strategies for Controlled
Regenerative Processes
. 186
6.6.
Adaptive Strategies for Controlled Regenerative Processes
. 196
Control of Markov Processes with Discrete Time
and Semi-Markov Processes
203
7.1.
Preliminary Results
. 203
7.2.
Optimal Automaton Control for Markov Processes with A Compact
State Space and A Finite Control Set
. 211
7.3.
Searching Optimal Strategies for Ergodic Markov Processes with
Compact Spaces of States and Controls
. 215
7.4.
Control of Finite Semi-Markov Processes
. 221
7.5.
Control of Countably Valued Semi-Markov Processes
. 225
7.6.
Optimal Control of Special Classes of Markov Processes
with Discrete Time
. 237
Control of Stationary Processes
251
8.1.
Formulation of the Problem
. 251
8.2.
Some Properties of Stationary Processes
. 252
8.3.
Auxiliary Results for CSP
. 254
8.4.
Adaptive Strategies for CSP
. 262
Finite-Converging Procedures for Control Problems
with Inequalities
267
9.1.
Formulation of the Problem
. 267
9.2.
Finite-converging Procedures of Solving A Countable System
of Inequalities
. 269
9.3.
Sufficient Conditions for Existence of FCP
. 273
Contents xv
9.4.
Stabilization of Solutions of Linear Difference
Equations: Part I
.276
9.5.
Stabilization of Solutions of Linear Difference
Equations: Part II
.281
10.
Control of Linear Difference Equations
287
10.1.
Auxiliary Results
. 287
10.2.
Control of Homogeneous Equations Xt+i
= Axt +
Вщ
. 297
10.3.
Optimal Tracking Problem for ARMAX
. 302
10.4.
Optimal Tracking and Consistency of Estimates for ARMAX
. . . 310
10.5.
Adaptive Modal Control
. 320
10.6.
On Strong Consistency of
LSE
and SGE of Parameters
. 328
10.7.
Linear-Quadratic Problem (LQP)
. 339
10.8.
LQP for ARMAX-type Equations
. 352
11.
Control of Ordinary Differential Equations
359
11.1.
Preliminary Results
. 359
11.2.
Control of Homogeneous Equations
. 365
11.3.
Control with A Model Reference
. 370
11.4.
Steepest Descent Method
. 381
11.5.
Stabilization of Solutions of Minimum Phase Equations
. 387
11.6.
Stabilization of Minimum Phase Equations
with Nonlinearities
. 395
11.7.
Stabilization of Linear Minimum Phase Equations
in Hubert Space
. 397
11.8.
Control of Stabilizable Equations
. 404
11.9.
Two Special Problems of Adaptive Control
. 413
12.
Control of Stochastic Differential Equations
421
12.1.
Preliminary Results
.421
12.2.
Stabilization of Solutions of Minimum Phase
Ito
Equations
. 430
12.3.
Identification Methods for
Ito
Equations
.439
12.4.
LQP for Stochastic
Ito
Equations
.441
Comments and Supplements
445
General References
459
Special References
461
Additional References
469
Index
471 |
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| id | DE-604.BV022969279 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:07:53Z |
| indexdate | 2024-07-09T21:08:50Z |
| institution | BVB |
| isbn | 9812563717 |
| language | English Russian |
| lccn | 2006298506 |
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| publisher | World Scientific |
| record_format | marc |
| series | Interdisciplinary mathematical sciences |
| series2 | Interdisciplinary mathematical sciences |
| spelling | Sragovič, Vladimir Grigorʹevič Verfasser aut Mathematical theory of adaptive control Vladimir G. Sragovich Singapore [u.a.] World Scientific 2006 XV, 473 S. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary mathematical sciences 4 Mathematisches Modell Control theory Mathematical models Adaptive control systems Adaptive Steuerung (DE-588)4112450-9 gnd rswk-swf Gesteuerter stochastischer Prozess (DE-588)4157166-6 gnd rswk-swf Adaptivregelung (DE-588)4000457-0 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Adaptivregelung (DE-588)4000457-0 s Stochastische Kontrolltheorie (DE-588)4263657-7 s Adaptive Steuerung (DE-588)4112450-9 s Gesteuerter stochastischer Prozess (DE-588)4157166-6 s DE-604 Interdisciplinary mathematical sciences 4 (DE-604)BV035420471 4 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016173550&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sragovič, Vladimir Grigorʹevič Mathematical theory of adaptive control Interdisciplinary mathematical sciences Mathematisches Modell Control theory Mathematical models Adaptive control systems Adaptive Steuerung (DE-588)4112450-9 gnd Gesteuerter stochastischer Prozess (DE-588)4157166-6 gnd Adaptivregelung (DE-588)4000457-0 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd |
| subject_GND | (DE-588)4112450-9 (DE-588)4157166-6 (DE-588)4000457-0 (DE-588)4263657-7 |
| title | Mathematical theory of adaptive control |
| title_auth | Mathematical theory of adaptive control |
| title_exact_search | Mathematical theory of adaptive control |
| title_exact_search_txtP | Mathematical theory of adaptive control |
| title_full | Mathematical theory of adaptive control Vladimir G. Sragovich |
| title_fullStr | Mathematical theory of adaptive control Vladimir G. Sragovich |
| title_full_unstemmed | Mathematical theory of adaptive control Vladimir G. Sragovich |
| title_short | Mathematical theory of adaptive control |
| title_sort | mathematical theory of adaptive control |
| topic | Mathematisches Modell Control theory Mathematical models Adaptive control systems Adaptive Steuerung (DE-588)4112450-9 gnd Gesteuerter stochastischer Prozess (DE-588)4157166-6 gnd Adaptivregelung (DE-588)4000457-0 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd |
| topic_facet | Mathematisches Modell Control theory Mathematical models Adaptive control systems Adaptive Steuerung Gesteuerter stochastischer Prozess Adaptivregelung Stochastische Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016173550&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035420471 |
| work_keys_str_mv | AT sragovicvladimirgrigorʹevic mathematicaltheoryofadaptivecontrol |