Lyapunov functions in differential games:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Taylor & Francis
2003
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| Series: | Stability and control
19 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 281 S. graph. Darst. |
| ISBN: | 0415273412 |
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| adam_text | LYAPUNOV FUNCTIONS IN DIFFERENTIAL GAMES VLADISLAV I. ZHUKOVSKIY THE
RUSSIAN CORRESPONDENCE INSTITUTE OF TEXTILE AND LIGHT INDUSTRIES,
MOSCOW, RUSSIA TAYLOR & FRANCIS TAYLOR & FRANCIS GROUP LONDON AND NEW
YORK CONTENTS INTRODUCTION TO THE SERIES IX PREFACE XI NOTATION XV 1
GENERAL NOTIONS AND EXAMPLES 1 1.0 INTRODUCTION 1 1.1 BASIC NOTIONS OF
THE THEORY OF DIFFERENTIAL GAMES UNDER UNCERTAINTY 2 1.1.1 ASPECTS OF
GAMES 2 1.1.2 DYNAMICAL ASPECTS 5 1.1.3 DE PRINCIPLIS NON EST
DISPUTANDUM 9 1.1.4 ECONOMIC INTERPRETATION OF THE GAME 10 1.1.5 CONTENT
OF THE THEORY 13 1.2 GAME PROBLEMS IN ECONOMIC AND MECHANICAL SYSTEMS 17
1.2.1 COMPETITION OF TWO ECONOMIES 17 1.2.2 TRACKING PROBLEMS 19 1.2.3
PROBLEM OF APPROACHING 22 VI CONTENTS 1.3 VECTOR GUARANTEES 25 1.3.1 AD
NARRANDUM, NON AD PROBUNDUM 25 1.3.2 FORMALIZATION OF THE VECTOR
GUARANTEES 29 1.3.3 GEOMETRIC INTERPRETATION OF THE VECTOR GUARANTEES
35 1.3.4 SUFFICIENT CONDITIONS 39 1.4 THE VECTOR GUARANTEES MAY NOT
EXIST 50 1.4.1 STATEMENT OF THE PROBLEM 50 1.4.2 LEMMA FOR
COUNTER-EXAMPLES 51 1.4.3 THE BELLMAN FUNCTION 58 1.4.4 THE CLASS OF
GAMES IN WHICH THE VECTOR GUARANTEES ARE ABSENT 59 1.5 CONVERSE PROBLEM
61 1.5.1 TRADITIONAL APPROACH 61 1.5.2 APPLICATION OF DYNAMICAL
PROGRAMMING 62 1.5.3 COMPARISON WITH THE MINIMAL GUARANTEE 71 1.6 THE
NASH EQUILIBRIUM FOR UNCERTAINTY 72 1.6.1 FORMALIZATION OF THE
EQUILIBRIUM 72 1.6.2 THE SUFFICIENT CONDITIONS 76 1.6.3 THE COEFFICIENT
CRITERIA 80 1.6.4 THE PROPERTIES OF THE ENSURING NASH EQUILIBRIA 83
EXERCISES 90 COMMENTS AND REFERENCES 94 2 OBJECTION AND
COUNTER-OBJECTION EQUILIBRIUM UNDER UNCERTAINTY 101 2.0 INTRODUCTION 101
2.1 PECULIARITIES OF THE NASH EQUILIBRIUM 102 2.1.1 THE NASH EQUILIBRIUM
SITUATION 102 2.1.2 PROPERTIES 103 2.1.3 PECULIARITIES 104 2.1.4 THE
CLASS OF GAMES IN WHICH THE NASH EQUILIBRIUM IS ABSENT 106 2.2
FORMALIZATION AND THE PROPERTIES OF UNIMPROVABLE EQUILIBRIA 108 2.2.1
COMPLETE AND INCOMPLETE COUNTER-OBJECTIONS 108 2.2.2 SOLUTIONS OF
THE MULTICRITERIA PROBLEM 109 2.2.3 FORMALIZATION OF UNIMPROVABLE
EQUILIBRIA 112 CONTENTS VII 2.2.4 THE PROPERTIES OF THE UNIMPROVABLE
EQUILIBRIA 114 2.2.5 EXISTENCE 116 2.3 COMPARISON WITH THE NASH
EQUILIBRIUM 125 2.3.1 NON-DOMINATION AND UNIMPROVABILITY 125 2.3.2 CLASS
OF GAMES, WHERE NO NASH EQUILIBRIUM EXISTS, BUT THE GEOFFRIONE
EQUILIBRIUM OF OBJECTIONS AND COUNTER-OBJECTIONS EXISTS 125 2.3.3
RELATIONSHIP WITH THE NASH EQUILIBRIUM 129 2.3.4 EXAMPLES 131 2.4
FORMALIZATION OF UNIMPROVABLE EQUILIBRIA IN THE DIFFERENTIAL GAME 138
2.4.1 MATHEMATICAL MODEL OF THE GAME 138 2.4.2 ANALOGUE OF VECTOR SADDLE
POINT 140 2.4.3 PROPERTIES 144 2.4.4 STABILITY 150 2.5 AUXILIARY
ASSERTIONS 151 2.5.1 COEFFICIENT CRITERIA 152 2.5.2 REDUCTION TO
NON-COOPERATION GAME 156 2.5.3 PROPERTIES OF MATRIX LINEAR CONVOLUTIONS
158 2.6 SUFFICIENT CONDITIONS FOR THE ANALOGUE OF A SADDLE POINT 160
2.6.1 APPLICATION OF DYNAMICAL PROGRAMMING 160 2.6.2 COEFFICIENT
CRITERIA 165 2.6.3 GAMES WITH SMALL PERTURBATIONS 171 2.7 UNIMPROVABLE
GUARANTEEING EQUILIBRIA (ANALOGUE OF THE VECTOR MAXIMIN) 175 2.7.1
COUNTER-EXAMPLE 175 2.7.2 FORMALIZATION OF UNIMPROVABLE EQUILIBRIA 180
2.7.3 PROPERTIES OF USEOC 187 2.8 ACTIVE EQUILIBRIUM UNDER UNCERTAINTY
196 2.8.1 FORMALIZATION OF SOLUTION 196 2.8.2 AUXILIARY ASSERTIONS 201
2.8.3 CONSTRUCTION OF THE SET ZF 205 2.8.4 DETERMINATION OF ACTIVE
EQUILIBRIUM OF THE GAME (2.7.14) 209 2.8.5 EXISTENCE CONDITIONS FOR UASE
216 2.8.6 EXAMPLE 220 VIII CONTENTS EXERCISES 226 COMMENTS AND
REFERENCES 232 APPLICATIONS 235 APPLICATION 1: SOME RESULTS FROM THE
THEORY OF DIFFERENTIAL EQUATIONS 235 APPLICATION 2: RESULTS FROM THE
THEORY OF QUADRATIC FORMS 237 APPLICATION 3: RESULTS FROM MATHEMATICAL
PROGRAMMING 239 APPLICATION 4: ADDITIONAL AUXILIARY ASSERTIONS 242
ANSWERS AND SOLUTIONS 249 REFERENCES 267 SUBJECT INDEX 279
|
| any_adam_object | 1 |
| author | Zukovskij, Vladislav I. |
| author_facet | Zukovskij, Vladislav I. |
| author_role | aut |
| author_sort | Zukovskij, Vladislav I. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:44Z |
| institution | BVB |
| isbn | 0415273412 |
| language | English |
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| owner_facet | DE-634 DE-11 |
| physical | XVI, 281 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Taylor & Francis |
| record_format | marc |
| series | Stability and control |
| series2 | Stability and control |
| spelling | Zukovskij, Vladislav I. Verfasser aut Lyapunov functions in differential games Vladislav I. Zhukovskiy London Taylor & Francis 2003 XVI, 281 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Stability and control 19 Ljapunov-Funktion (DE-588)4274502-0 gnd rswk-swf Differentialspiel (DE-588)4012253-0 gnd rswk-swf Ljapunov-Funktion (DE-588)4274502-0 s Differentialspiel (DE-588)4012253-0 s DE-604 Stability and control 19 (DE-604)BV010641392 19 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017479540&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zukovskij, Vladislav I. Lyapunov functions in differential games Stability and control Ljapunov-Funktion (DE-588)4274502-0 gnd Differentialspiel (DE-588)4012253-0 gnd |
| subject_GND | (DE-588)4274502-0 (DE-588)4012253-0 |
| title | Lyapunov functions in differential games |
| title_auth | Lyapunov functions in differential games |
| title_exact_search | Lyapunov functions in differential games |
| title_full | Lyapunov functions in differential games Vladislav I. Zhukovskiy |
| title_fullStr | Lyapunov functions in differential games Vladislav I. Zhukovskiy |
| title_full_unstemmed | Lyapunov functions in differential games Vladislav I. Zhukovskiy |
| title_short | Lyapunov functions in differential games |
| title_sort | lyapunov functions in differential games |
| topic | Ljapunov-Funktion (DE-588)4274502-0 gnd Differentialspiel (DE-588)4012253-0 gnd |
| topic_facet | Ljapunov-Funktion Differentialspiel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017479540&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010641392 |
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