Fixed duration pursuit-evasion differential game with integral constraints

We investigate a pursuit-evasion differential game of countably many pursuers and one evader. Integral constraints are imposed on control functions of the players. Duration of the game is fixed and the payoff of the game is infimum of the distances between the evader and pursuers when the game is completed. Purpose of the pursuers is to minimize the payoff and that of the evader is to maximize it. Optimal strategies of the players are constructed, and the value of the game is found. It should be noted that energy resource of any pursuer may be less than that of the evader

On a linear differential game of optimal approach of many pursuers with one evader

We consider a differential game of approach of many pursuers and one evader. The motions of all players are described by linear systems of the same type. Control functions of players are subject to integral constraints. The duration of the game is fixed. The payoff functional of the differential game is the minimum of the distances between the evader and the pursuers when the game terminates. The pursuers try to minimize the payoff functional, and the evader tries to maximize it. We obtain estimates for the payoff functional of the game, which can be guaranteed by players and explicitly describe the strategies of the players. From here we obtain that in some specific cases the value of the game exists, and optimal strategies can be constructed. An illustrative example is considered