Simple motion pursuit differential game of many pursuers and one evader on convex compact set

A pursuit differential game of m pursuers and single evader in nonempty closed bounded convex subset of Rn is studied. At this juncture, all players must not leave the given set A which is subset of Rn and control parameters of all players are subjected to geometric constraints. All players move with speeds less than or equal to 1. We say that pursuit is completed if geometric position of at least one pursuer coincides with that of the evader. In this game, pursuers try to complete the pursuit. The problem of this study is to obtain the estimation for guaranteed pursuit time (GPT). To solve this problem, first, we construct strategies for the pursuers in ndimensional cube. Then, reduce the problem to the game in the cube and apply the method of fictitious pursuers. In this thesis, we improve the estimation of GPT from third degree polynomial O(n3) to second degree polynomial O(n2).

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