Optimal control of random sequences in problems with constraints:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Mathematics and its applications
410 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 345 S. graph. Darst. |
| ISBN: | 0792345711 |
Staff View
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| 245 | 1 | 0 | |a Optimal control of random sequences in problems with constraints |c by A. B. Piunovskiy |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1997 | |
| 300 | |a XI, 345 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a commande optimale |2 inriac | |
| 650 | 7 | |a commande stochastique |2 inriac | |
| 650 | 7 | |a contrainte |2 inriac | |
| 650 | 7 | |a méthode Bellman |2 inriac | |
| 650 | 7 | |a problème quadratique linéaire |2 inriac | |
| 650 | 7 | |a processus Markov |2 inriac | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Mathematical optimization | |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Preface xi
Introduction 1
Chapter 1 Methods of Stochastic Optimal Control 7
1.1 Statement of the optimal control problem and examples 7
1.1.1 Description of the controlled stochastic process 7
1.1.2 Construction of mathematical models 11
1.1.3 Optimal control problems 21
1.1.4 Methods for solving of the problems with an integral 27
functional
1.2 Markov decision processes 31
1.2.1 Markov model with a finite horizon 31
1.2.2 Discounted Markov model 49
1.2.3 Markov model with the average loss 64
Chapter 2 Optimal Control Problems with Constraints 77
2.1 Statement of the problem 77
2.1.1 Main convex programming problem 77
2.1.2 Convexity of the main functional 78
2.1.3 Example 79
2.2 Properties of the strategic measures space 80
2.2.1 Convexity and measurability 80
2.2.2 Closure 81
2.2.3 Structure of extreme points in V 83
2.2.4 Everywhere dense subset in V 89
2.2.5 Example 92
2.3 Necessary and sufficient conditions for optimality 96
2.3.1 Lagrange function and similar issues 96
vii
2.3.2 Conditions of optimality 97
2.4 Essential and inessential constraints 98
2.4.1 Necessary and sufficient conditions of the essence 98
2.4.2 Essential constraints and Pareto optimal solutions 100
2.5 Algorithm for solving the main convex programming 103
problem
2.5.1 Problem with integral functionals 103
2.5.2 Auxiliary results 104
2.5.3 Description of the algorithm 107
2.5.4 Discussion of the applicability of the algorithm 110
2.6 Example 111
Chapter 3 Solvability of the main constrained 123
problem and some extensions
3.1 Existence of solutions in constrained problems 123
3.1.1 General solvability theorem 123
3.1.2 Models with the integral functionals 125
3.1.3 Markov model with the average losses 127
3.1.4 Application of linear programming methods 131
3.2 Form of optimal control strategies 132
3.2.1 Sufficiency of extreme points 133
3.2.2 Sufficiency of finite mixtures of selectors 134
3.2.3 Optimal strategies in Markov models 136
3.2.4 Convex Markov models and 152
sufficiency of Markov selectors
3.3 Example 156
3.3.1 Discrete queueing system 156
3.3.2 Concave and convex modifications 159
3.4 Other constrained problems of optimal control 165
3.4.1 Problems with partial information 165
3.4.2 Optimization in the class of selectors 168
3.4.3 Markov models with dissimilar functionals 172
3.4.4 Unbounded loss functionals and other extensions 175
viii
Chapter 4 Linear quadratic systems 179
4.1 Model with a finite horizon 179
4.1.1 Statement of the problem 180
4.1.2 General results 182
4.1.3 Problem solving (alternative I) 186
4.1.4 Problem solving (alternative II) 189
4.2 Homogeneous discounted model 194
4.2.1 Statement of the problem 194
4.2.2 General results 197
4.2.3 Problem solving (alternative I) 206
4.2.4 Problem solving (alternative II) 208
4.3 Homogeneous model with average losses 209
4.3.1 Statement of the problem 209
4.3.2 General results 211
4.3.3 Problem solving (alternative I) 216
4.3.4 Problem solving (alternative II) 217
Chapter 5 Some applications 219
5.1 Stochastic macroeconomic model of the Neumann type 219
5.1.1 Model description 220
5.1.2 Problem solving 222
5.1.3 Essence of constraints, non negativeness of the actions, 226
and other questions
5.2 Simplest ecological economic system 229
5.2.1 Insulated economic subsystem 229
5.2.2 Model description and statement of the problem 231
5.2.3 Construction of quasi optimal control strategies 235
5.2.4 Numerical example 238
5.3 Model of insurance 242
5.3.1 Model description 242
5.3.2 General results 246
5.3.3 Problem solving (alternative I) 249
5.3.4 Problem solving (alternative II) 251
5.4 Stochastic stabilization problem 253
5.4.1 Problem statement 253
ix
5.4.2 General results 255
5.4.3 Problem solving (alternatives I and II) 256
5.4.4 Pareto set 258
5.5 Queueing system 260
5.5.1 Model description 260
5.5.2 General results 263
5.5.3 Problem solving (alternative I) 265
5.5.4 Problem solving (alternative II) 267
5.6 Optimization of publicity expenses 269
5.6.1 Problem statement 270
5.6.2 General results 271
5.6.3 Problem solving (alternative I) 272
5.6.4 Problem solving (alternative II) 274
5.6.5 Pareto set 276
5.7 Simplest constrained game 278
5.7.1 Description of the game 278
5.7.2 General results 279
5.7.3 Problem solving (alternative I) 281
5.7.4 Problem solving (alternative II) 286
Conclusion 290
Appendix 291
Al Borel spaces and their properties 291
Al.l Main concepts 291
A1.2 Probability measures on Borel spaces 293
A 1.3 Semicontinuous functions and measurable selection 295
A2 Elements of convex analysis 297
A2.1 Certain definitions 297
A2.2 Duality relation and Kuhn Tucker theorem 299
A2.3 Selected properties of convex sets 300
A3 Proofs of auxiliary statements 301
A4 Linear quadratic systems: proofs of some statements 313
References 327
Index 337
List of symbols 341
List of the main statements 343
x
|
| any_adam_object | 1 |
| author | Piunovskij, Alexei B. |
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| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8/312 |
| dewey-search | 629.8/312 |
| dewey-sort | 3629.8 3312 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| id | DE-604.BV011655883 |
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| indexdate | 2024-07-09T18:13:32Z |
| institution | BVB |
| isbn | 0792345711 |
| language | English |
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| physical | XI, 345 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| publisher | Kluwer |
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| spelling | Piunovskij, Alexei B. Verfasser (DE-588)1029167125 aut Optimal control of random sequences in problems with constraints by A. B. Piunovskiy Dordrecht [u.a.] Kluwer 1997 XI, 345 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 410 Commande , Théorie de la ram commande optimale inriac commande stochastique inriac contrainte inriac méthode Bellman inriac problème quadratique linéaire inriac processus Markov inriac Control theory Mathematical optimization Stochastic processes Stochastische optimale Kontrolle (DE-588)4207850-7 gnd rswk-swf Zufällige Folge (DE-588)4191092-8 gnd rswk-swf Restriktion Mathematik (DE-588)4177885-6 gnd rswk-swf Zufällige Folge (DE-588)4191092-8 s Stochastische optimale Kontrolle (DE-588)4207850-7 s Restriktion Mathematik (DE-588)4177885-6 s DE-604 Mathematics and its applications 410 (DE-604)BV008163334 410 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007857500&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Piunovskij, Alexei B. Optimal control of random sequences in problems with constraints Mathematics and its applications Commande , Théorie de la ram commande optimale inriac commande stochastique inriac contrainte inriac méthode Bellman inriac problème quadratique linéaire inriac processus Markov inriac Control theory Mathematical optimization Stochastic processes Stochastische optimale Kontrolle (DE-588)4207850-7 gnd Zufällige Folge (DE-588)4191092-8 gnd Restriktion Mathematik (DE-588)4177885-6 gnd |
| subject_GND | (DE-588)4207850-7 (DE-588)4191092-8 (DE-588)4177885-6 |
| title | Optimal control of random sequences in problems with constraints |
| title_auth | Optimal control of random sequences in problems with constraints |
| title_exact_search | Optimal control of random sequences in problems with constraints |
| title_full | Optimal control of random sequences in problems with constraints by A. B. Piunovskiy |
| title_fullStr | Optimal control of random sequences in problems with constraints by A. B. Piunovskiy |
| title_full_unstemmed | Optimal control of random sequences in problems with constraints by A. B. Piunovskiy |
| title_short | Optimal control of random sequences in problems with constraints |
| title_sort | optimal control of random sequences in problems with constraints |
| topic | Commande , Théorie de la ram commande optimale inriac commande stochastique inriac contrainte inriac méthode Bellman inriac problème quadratique linéaire inriac processus Markov inriac Control theory Mathematical optimization Stochastic processes Stochastische optimale Kontrolle (DE-588)4207850-7 gnd Zufällige Folge (DE-588)4191092-8 gnd Restriktion Mathematik (DE-588)4177885-6 gnd |
| topic_facet | Commande , Théorie de la commande optimale commande stochastique contrainte méthode Bellman problème quadratique linéaire processus Markov Control theory Mathematical optimization Stochastic processes Stochastische optimale Kontrolle Zufällige Folge Restriktion Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007857500&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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