Differential games of pursuit:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1993
|
| Schriftenreihe: | Series on optimization
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | IX, 325 S. graph. Darst. |
| ISBN: | 9810209797 |
Internformat
MARC
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| 100 | 1 | |a Petrosjan, Leon A. |d 1940- |e Verfasser |0 (DE-588)123918049 |4 aut | |
| 245 | 1 | 0 | |a Differential games of pursuit |c Leon A. Petrosjan |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1993 | |
| 300 | |a IX, 325 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on optimization |v 2 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Differential games | |
| 650 | 0 | 7 | |a Differentialspiel |0 (DE-588)4012253-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialspiel |0 (DE-588)4012253-0 |D s |
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| 940 | 1 | |n oe | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006311105 | |
Datensatz im Suchindex
| _version_ | 1820173247476400128 |
|---|---|
| adam_text |
Contents
Preface viii
1 Preliminaries 1
1.1 Zero-sum two-person games in normal form 1
1.2 Equilibrium Point 9
1.3 Mixed strategies and existence of equilibrium point 17
1.4 Games with convex payoff function 20
1.5 One class of games with complete information 32
1.6 Simultaneous games of pursuit with non-convex payoff
functions 38
2 Definition of differential game of pursuit and existence theo¬
rem of equilibrium points 49
2.1 Nonformal description 49
2.2 Game of pursuit in normal form 53
2.3 Existence of the e-equilibrium point in differential games with
prescribed duration 59
2.4 Existence of e-equilibrium points in optimal time differential
pursuit games 66
2.5 Alternative 71
2.6 Differential games with dependent motions 73
2.7 Alternative for games with dependent motions and
discrimination 80
3 Class of pursuit—evasion games with optimal open—loop strat¬
egy for evader 83
3.1 Discrete game with terminal payoff and discrimination for
player E 83
3.2 Continuous game without discrimination 90
3.3 Arbitrary terminal payoff functions and phase constrains . 92
3.4 Optimal time pursuit games 95
v
vi Contents
3.5 Necessary and sufficient conditions for existance of optimal open-
loop strategy for player E 104
3.6 Iterative methods for solution of differential game of pursuit . . 110
4 Examples of differential games of pursuit 119
4.1 Games with prescribed duration without phase constraints . . .119
4.2 Phase-constrained "simple pursuit" games 131
4.3 "Simple pursuit" game with two pursuers and one evader . . . .138
4.4 Relations between maximin time of pursuit and time of
absorption 143
5 "Life line" game of pursuit 149
5.1 Definition of "life line" game 149
5.2 Discrete game 150
5.3 Proof of one geometric lemma 153
5.4 Basic theorem 157
5.5 Rejection of discrimination 158
5.6 Multiplayer "life line" games 162
6 Differential games with incomplete information 169
6.1 Pursuit games with delayed information for player P 169
6.2 Game with information delayed. Case of m pursuiers and one
evader 177
6.3 Existence of equilibria in mixed strategies in "princess and mon¬
ster" game of pursuit 182
6.4 Differential games with discrete information partition 191
6.5 Games with mixed information state 199
6.6 Pursuit game with prescribe duration and delayed information
for both players 207
6.7 Delayed information for both players when the evader team
takes part in game 211
6.8 One multistage game with delayed information 226
7 Noncooperative differential games 235
7.1 Game on a finite graph tree 235
7.2 Nash equilibrium 239
7.3 Definition of the noncooperative differential games in normal
form 253
7.4 Definition of cooperative differential game in the form of char¬
acteristic sets 257
7.5 Classification of dinamic stable (time-consistant) solutions . . . 261
Contents vii
7.6 Structure and dynamic stability of pareto optimal solution in
the game of approaching 270
7.7 Existence of dynamic stable C-kemel and iVM-solution in co¬
operative game of approaching 278
8 Cooperative differential games with side payments 283
8.1 Definition of cooperative differential game in the characteristic
function form 283
8.2 Principle of dynamic stability (time-consistancy) 289
8.3 Classification of dynamic stable solutions 298
9 New optimality principles in n—person differential games 303
9.1 Integral optimality principles 303
9.2 Differential strongly time consistent optimality principles . . . .311
9.3 Strongly time consistent optimality principles for the games
with discount payoffs 315
Bibliography 319
Index 325 |
| any_adam_object | 1 |
| author | Petrosjan, Leon A. 1940- |
| author_GND | (DE-588)123918049 |
| author_facet | Petrosjan, Leon A. 1940- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009552490 |
| illustrated | Illustrated |
| indexdate | 2025-01-02T21:14:37Z |
| institution | BVB |
| isbn | 9810209797 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006311105 |
| oclc_num | 489022167 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-11 |
| owner_facet | DE-12 DE-703 DE-11 |
| physical | IX, 325 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on optimization |
| series2 | Series on optimization |
| spelling | Petrosjan, Leon A. 1940- Verfasser (DE-588)123918049 aut Differential games of pursuit Leon A. Petrosjan Singapore [u.a.] World Scientific 1993 IX, 325 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on optimization 2 Aus dem Russ. übers. Differential games Differentialspiel (DE-588)4012253-0 gnd rswk-swf Differentialspiel (DE-588)4012253-0 s DE-604 Series on optimization 2 (DE-604)BV009552485 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006311105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petrosjan, Leon A. 1940- Differential games of pursuit Series on optimization Differential games Differentialspiel (DE-588)4012253-0 gnd |
| subject_GND | (DE-588)4012253-0 |
| title | Differential games of pursuit |
| title_auth | Differential games of pursuit |
| title_exact_search | Differential games of pursuit |
| title_full | Differential games of pursuit Leon A. Petrosjan |
| title_fullStr | Differential games of pursuit Leon A. Petrosjan |
| title_full_unstemmed | Differential games of pursuit Leon A. Petrosjan |
| title_short | Differential games of pursuit |
| title_sort | differential games of pursuit |
| topic | Differential games Differentialspiel (DE-588)4012253-0 gnd |
| topic_facet | Differential games Differentialspiel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006311105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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