Differential Games of Pursuit

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World Scientific, 1993 - Mathematics - 325 pages
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The classical optimal control theory deals with the determination of an optimal control that optimizes the criterion subjects to the dynamic constraint expressing the evolution of the system state under the influence of control variables. If this is extended to the case of multiple controllers (also called players) with different and sometimes conflicting optimization criteria (payoff function) it is possible to begin to explore differential games. Zero-sum differential games, also called differential games of pursuit, constitute the most developed part of differential games and are rigorously investigated. In this book, the full theory of differential games of pursuit with complete and partial information is developed. Numerous concrete pursuit-evasion games are solved (”life-line” games, simple pursuit games, etc.), and new time-consistent optimality principles in the n-person differential game theory are introduced and investigated.
 

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Contents

the game of approaching 270
7
Definition of differential game of pursuit and existence theo
49
Class of pursuitevasion games with optimal openloop strat
83
Examples of differential games of pursuit
119
Life line game of pursuit
149
Differential games with incomplete information
169
Noncooperative differential games
235
Cooperative differential games with side payments
283
New optimality principles in nperson differential games
303
Bibliography
319
Index
325
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