Screen LibraryDifferential games of pursuit /
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...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; River Edge, N.J. : |
| Publication Dates: | 1993. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Series on optimization ;
vol. 2 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/1670#t=toc |
| Summary: |
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. |
| Carrier Form: | 1 online resource (ix,325pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 319-324) and index. |
| ISBN: | 9789814355834 (electronic bk.) |
| Index Number: | QA272 |
| CLC: | O225 |
| Contents: | 1. Preliminaries. 1.1. Zero-sum two-person games in normal form -- 1.2. Equilibrium point -- 1.3. Mixed strategies and existence of equilibrium point -- 1.4. Games with convex payoff function -- 1.5. One class of games with complete information -- 1.6. Simultaneous games of pursuit with non-convex payoff functions -- 2. Definition of differential game of pursuit and existence theorem of equilibrium points. 2.1. Nonformal description -- 2.2. Game of pursuit in normal form -- 2.3. Existence of the t-equilibrium point in differential games with prescribed duration -- 2.4. Existence of e-equilibrium points in optimal time differential pursuit games -- 2.5. Alternative -- 2.6. Differential games with dependent motions -- 2.7. Alternative for games with dependent motions and discrimination -- 3. Class of pursuit evasion games with optimal open loop strategy for evader. 3.1. Discrete game with terminal payoff and discrimination for player E -- 3.2. Continuous game without discrimination -- 3.3. Arbitrary terminal payoff functions and phase constrains -- 3.4. Optimal time pursuit games -- 3.5. Necessary and sufficient conditions for existance of optimal open-loop strategy for player E -- 3.6. Iterative methods for solution of differential game of pursuit -- 4. Examples of differential games of pursuit. 4.1. Games with prescribed duration without phase constraints -- 4.2. Phase-constrained "simple pursuit" games -- 4.3. "Simple pursuit" game with two pursuers and one evader -- 4.4. Relations between maxirnin time of pursuit and time of absorption -- 5. "Life line" game of pursuit. 5.1. Definition of "life line" game -- 5.2. Discrete game -- 5.3. Proof of one geometric lemma -- 5.4. Basic theorem -- 5.5. Rejection of discrimination -- 5.6. Multiplayer "lifeline" games -- 6. Differential games with incomplete information. 6.1. Pursuit games with delayed information for player P -- 6.2. Game with information delayed. Case of m pursuiers and one evader -- 6.3. Existence of equilibria in mixed strategies in "princess and monster" game of pursuit -- 6.4. Differential games with discrete information partition -- 6.5. Games with mixed information state -- 6.6. Pursuit game with prescribe duration and delayed information for both players -- 6.7. Delayed information for both players when the evader team takes part in game -- 6.8. One multistage game with delayed information -- 7. Noncooperative differential games. 7.1. Game on a finite graph tree -- 7.2. Nash equilibrium -- 7.3. Definition of the noncooperative differential games in normal form -- 7.4. Definition of cooperative differential game in the form of characteristic sets -- 7.5. Classification of dinamic stable (time-consistant) solutions -- 7.6. Structure and dynamic stability of pareto optimal solution in the game of approaching -- 7.7. Existence of dynamic stable C-kernel and NM-solution in cooperative game of approaching -- 8. Cooperative differential games with side payments. 8.1. Definition of cooperative differential game in the characteristic function form -- 8.2. Principle of dynamic stability (time-consistancy) -- 8.3. Classification of dynamic stable solutions -- 9. New optimality principles in n-person differential games. 9.1. Integral optimality principles -- 9.2. Differential strongly time consistent optimabty principles -- 9.3. Strongly time consistent optimality principles for the games with discount payoffs. |