The Pursuit–Evasion problems in a differential game with GGr-constraints on controls

In the present paper, we consider pursuit and evasion problems in a simple motion differential game when Pursuer's control is subjected to geometric constraint and Evader's control is subjected to Grönwall type constraint. In order to solve the pursuit problem, the parallel convergence strategy (the П-strategy) for the Pursuer is constructed, and sufficient conditions of pursuit are obtained. Also, we prove that the П-strategy is an optimal strategy of Pursuer. In solving of the evasion problem, we propose an admissible control function to the Evader, and we obtaine sufficient conditions of evasion. In addition, an estimation of the distance between the objects during the game is provided.

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