Minimization of resource stock in an impulse differential game with a non-convex terminal set

We consider a linear differential game of a given duration. Reachable sets of players are $n$-dimensional balls. An impulse constraint is imposed on the choice of the first player's control. Abilities of the first player are determined by the stock of resources that can be used by the player at formation of his control. Control of the second player has geometrical constraints. The terminal set of a game is determined by a condition for assigning the norm of a phase vector to a segment with positive ends. The goal of the first player is to lead a phase vector to the terminal set at fixed time. The goal of the second player is opposite. This article solves the problem of finding the smallest initial stock of resources at which the first player can guarantee the achievement of his goal.