A differential game with integral constraints in a half space.

We study a pursuit-evasion differential game of one pursuer and one evader in a half-space. On control functions of the players integral constraints are imposed. Duration of the game T is fixed. If at this time the state of the pursuer coincides with that of the evader then pursuit is considered completed. The state of the evader at the time T must belong to the half-space. In this game, the goal of the pursuer is to complete the pursuit as soon as possible, whereas the evader E wants to maximize the capture time. The evader uses information about the state of the pursuer only, whereas the pursuer uses the current value of the evader’s control parameter. The main result of this paper is the solution of the pursuit-evasion differential game. It should be noted that the energy recourse of the evader can be less than that of the pursuer. This theorem enables us to obtain the solution of the differential game problem with many pursuers.

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