Pursuit differential game of many pursuers and one evader in a convex hyperspace

A pursuit differential game of many pursuers and one evader in a nonempty closed convex compact hyperspace is studied.  Pursuit is completed when at least one pursuer coincides with the evader.  Control functions of players are constrained by geometric constraints.  A pursuit game in a set containing a closed convex compact set is solved, and pursuit is shown to be completed in a pursuit game within a finite-dimensional cube.  Parallel strategy and fictitious pursuers are used to solve the game, and a guaranteed pursuit time is obtained.

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