## Differential Games of PursuitThe 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 |

319 | |

325 | |

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### Common terms and phrases

arbitrary Assume auxiliary game behavior strategy called capture of Player capture point Cartesian product center of pursuit choice circle coalition coincides compact sets completes the proof conditionally optimal trajectory continuous function convex convex hull convex set corresponding defined definition Denote differential game distance dynamic stable e-optimal equilibrium point Euclidean distance evader Example existence finite number game F game F(y game is equal game of pursuit game terminates hence imputation information set initial conditions intersection interval Lemma measurable open-loop controls mixed strategies Motion equations MPOLBS Nash equilibrium open-loop control u(t partition payoff function payoff is equal payoff of Player piecewise open-loop strategies Player E's payoff prescribed duration probability measure prove pure strategy pursuer pursuit game radius reachability set satisfied sequence simple pursuit singular surface situation solution straight line strategy for Player strategy sets subgame terminal payoff trajectory x(t unique vector y(tk