Differential games: a concise introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2015
|
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 322 S. |
| ISBN: | 9789814596220 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Differential
GBaom©
A Concise Introduction
This book uses a small volume to present the most basic results
for deterministic two-person differential games. The presentation
begins with optimization of a single function, followed by a
basic theory for two-person games. For dynamic situations,
the author first recalls control theory which is treated as single-
person differential games. Then a systematic theory of two-person
differential games is concisely presented, including evasion and
pursuit problems, zero-sum problems and LQ differential games.
The book is intended to be self-contained, assuming that the readers
have basic knowledge of calculus, linear algebra, and elementary
ordinary differential equations. The readership of the book could
be junior/senior undergraduate and graduate students with majors
related to applied mathematics, who are interested in differential
games. Researchers in some other related areas, such as engineering,
social science, etc. will also find the book useful.
Contents
R
Preface vii
1. Introduction 1
1.1 Optimization Problems ..................................... 1
1.2 Game Theory — A Brief Glance............................... 3
1.2.1 Pareto optimum and Nash equilibrium................ 4
1.2.2 Two-person zero-sum game.......................... 11
1.3 Control and Differential Game Problems.................... 14
1.3.1 Control problems.................................. 15
1.3.2 Differential game problems........................ 20
1.4 Some Mathematical Preparations............................ 23
1.5 Brief Historic Remarks.................................... 36
2. Control Theory — Single-Player Differential Games 37
2.1 Control Systems........................................... 37
2.2 Optimal Control — Existence Theory........................ 39
2.3 Pontryagin Maximum Principle — A Variational
Method.................................................... 42
2.4 Dynamic Programming and HJB Equation ..................... 48
2.5 Viscosity Solutions....................................... 54
2.6 Autonomous Systems — Controllability Problems .... 63
2.6.1 Controllability................................... 64
2.6.2 Time optimal control problem...................... 76
2.6.3 Optimal control problem with first exit time ... 80
2.6.4 Stationary HJB equations ......................... 88
2.7 Viability Problems........................................ 93
xi
Differential Games — A Concise Introduction
2.8 Non-Uniqueness of Solutions to HJ Equations*.............. 97
2.9 Brief Historic Remarks...................................... 103
Two-Person Zero Sum Differential Games — A General
Consideration 105
3.1 Strategies.................................................. 105
3.2 Open-Loop Pareto Optima and Nash Equilibria................. 108
3.3 Two-Person Zero-Sum Differential Games...................... 109
3.4 Brief Historic Remarks.................................... 121
Differential Games with Unbounded Controls 123
4.1 Unbounded Controls.......................................... 123
4.2 Upper and Lower Hamiltonians................................ 125
4.3 Uniqueness of Viscosity Solution............................ 129
4.4 Upper and Lower Value Functions............................. 138
4.4.1 State trajectories and Elliott-Kalton strategies . . 138
4.4.2 Upper and lower value functions, and optimality
principle........................................... 142
4.4.3 Continuity of upper and lower value functions . . 148
4.5 Brief Historic Remarks...................................... 151
Differential Games of Pursuit and Evasion 153
5.1 Differential Pursuit Games ................................. 154
5.1.1 Captur ability...................................... 154
5.1.2 Characterization of capturable set.................. 162
5.2 Differential Evasion Games.................................. 167
5.2.1 Evadability......................................... 167
5.2.2 Characterization of evadable set.................... 177
5.3 Brief Historic Remarks...................................... 178
Linear-Quadratic Differential Games 181
6.1 Linear-Quadratic Optimal Control Problems .................. 181
6.1.1 Open-loop controls ................................. 183
6.1.2 A functional analysis approach*..................... 185
6.1.3 A two-point boundary value problem.................. 194
6.1.4 Closed-loop strategies.............................. 198
6.2 Differential Games.......................................... 214
6.3 A Quadratic Game in a Hilbert Space*........................ 224
Contents xiii
6.4 Open-Loop Saddle Points and Two-Point Boundary
Value Problems............................................... 228
6.5 Closed-Loop Saddle Points and Riccati Equations.............. 232
6.6 Solution to LQ Differential Games............................ 238
6.6.1 Closed-loop saddle point.......................... 238
6.6.2 One-dimensional case.............................. 241
6.6.3 Open-loop values and saddle point................. 247
6.7 Fredholm Integral Equation................................... 254
6.8 Brief Historic Remarks....................................... 258
7. Differential Games with Switching Strategies 259
7.1 Optimal Switching Control Problems........................... 259
7.1.1 Switching controls................................ 259
7.1.2 Dynamic programming and quasi-variational
inequality........................................... 265
7.1.3 Viscosity solutions of quasi-variational inequalities 270
7.2 Differential Games with Switching Controls................... 286
7.2.1 Bilateral obstacle quasi-variational inequality . . . 292
7.2.2 Existence of the value function................... 297
7.2.3 A limiting case................................... 307
7.3 Brief Historic Remarks....................................... 309
Bibliography 311
Index 319
|
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| author | Yong, Jiongmin 1958- |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042612555 |
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| institution | BVB |
| isbn | 9789814596220 |
| language | English |
| lccn | 014038343 |
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| oclc_num | 930986300 |
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| owner | DE-703 DE-634 DE-824 |
| owner_facet | DE-703 DE-634 DE-824 |
| physical | XIII, 322 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Yong, Jiongmin 1958- Verfasser (DE-588)121010481 aut Differential games a concise introduction Jiongmin Yong New Jersey [u.a.] World Scientific 2015 XIII, 322 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Differential games Game theory Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Spieltheorie (DE-588)4056243-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028045405&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028045405&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yong, Jiongmin 1958- Differential games a concise introduction Differential games Game theory Kontrolltheorie (DE-588)4032317-1 gnd Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4056243-8 |
| title | Differential games a concise introduction |
| title_auth | Differential games a concise introduction |
| title_exact_search | Differential games a concise introduction |
| title_full | Differential games a concise introduction Jiongmin Yong |
| title_fullStr | Differential games a concise introduction Jiongmin Yong |
| title_full_unstemmed | Differential games a concise introduction Jiongmin Yong |
| title_short | Differential games |
| title_sort | differential games a concise introduction |
| title_sub | a concise introduction |
| topic | Differential games Game theory Kontrolltheorie (DE-588)4032317-1 gnd Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Differential games Game theory Kontrolltheorie Spieltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028045405&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028045405&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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