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Series on Optimization - Vol. 2
DIFFERENTIAL GAMES OF PURSUIT
by Leon A Petrosjan (St. Petersburg State University, Russia)
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.
Contents:
- Preliminaries
- Definition of Differential Game of Pursuit
and Existence Theorem of Equilibrium Points
- Class of Pursuit-Evasion Games with Optimal Open-Loop Strategy for Evader
- Examples of Differential Games of Pursuit
- "Life Line" Game of Pursuit
- Differential Games with Incomplete Information
- Noncooperative Differential Games
- Cooperative Differential Games with Side Payments
- New Optimality Principles in n-Person Differential Games
Readership: Postgraduates and researchers in applied mathematics.
| 340pp |
Pub. date: Sept 1993 |
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