Relative optimal evasion time in the differential game of three pursuers and one evader in the plane.

We study a simple-motion pursuit-evasion differential game problem of three pursuers and one evader in the plane. All players have equal dynamical possibilities. The initial position of the evader is in the convex hull of the initial positions of the pursuers. All pursuers use the strategy of parallel approach. The differential game is considered completed if the state of a pursuer coincides with that of the evader. It was shown by Pshenichnii that pursuit can be completed in this differential game. We consider a differential game problem where the evader tries to maximize the guaranteed evasion time. In this paper, we obtained an explicit formula for the relative optimal evasion time and constructed a strategy for the evader.

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