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Game problem on a convex closed set. (English) Zbl 1138.91349

Summary: The movements of Pursuer P and Evader E in n are described by the equations P: x ˙=a(t)u and E: y ˙=a(t)v, where u and v are control parameters of P and E. A closed convex subset S of n is given. The players P and E must not leave S. Integral restrictions are imposed on the controls of the players. For arbitrary initial locations x 0 ,y 0 S of the players, the optimal time of pursuit is found and optimal strategies for the players are constructed.

This is an English translation of the author’s article [Mat. Tr. 4, No. , 96-112 (2001; Zbl 0998.91006)].

MSC:
91A23Differential games (game theory)
91A24Positional games