Towards a relaxation of the pursuit-evasion differential game

摘要

We consider a special case of the non-linear zero-sum pursuit-evasion differential game. The instance of this game is defined by two closed sets - target set and one specifying state constraints. We find an optimal non-anticipating strategy for player I (the pursuer). Namely, we construct his successful solvability set specified by limit function of the iterative procedure in space of positions. For positions located outside the successful solvability set, we provide a relaxation of our game by determining the smallest size of a neighborhoods of two mentioned sets, for which the pursuer can solve his problem successfully. Then, we construct his successful solvability set in terms of those neighborhoods.