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Two pursuers and one evader in the plane: A stochastic pursuit-evasion differential game

✍ Scribed by Y. Yavin


Publisher
John Wiley and Sons
Year
1986
Tongue
English
Weight
499 KB
Volume
7
Category
Article
ISSN
0143-2087

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✦ Synopsis


A stochastic pursuit-evasion differential game involving three players moving in the plane is considered. The players are E, the evader, and Pi (where i = 1,2), the pursuers. It is assumed that all players have complete observation of each other's positions. Also, each of the pursuers has a killing range and a detection range. If player E is intercepted by at least one of the pursuers before leaving the detection range of either of them, then the pursuers win the game. If, on the other hand, E leaves the detection range of one (or both) of the pursuers before being intercepted, then player E wins the game. Sufficient conditions on max-min pursuit-evasion strategies are derived. These conditions require the existence of a properly smooth solution to a non-linear partial differential equation on a torus in R 3 . By applying a finite-difference method, the equation is solved numerically, and the max-min pursuit-evasion strategies are computed.