Construction of optimal position strategies in a differential pursuit-evasion game with one pursuer and two evaders

The game-theoretic pursuit-evasion problem of one pursuer and two evaders is considered. It is assumed that one of the evaders must leave the game (disappear) at some time; however, neither this time nor the leaving evader is known in advance. The dynamics of all the objects can be described by the equations of the well-known Isaacs problem of the ''game of two cars'' [1] subject to conditions of restricted manoeuvrability of the objects. The minimum time difference between the pursuer and the evader remaining in the game is the payoff of the game. Under certain assumptions, relating the parameters of the objects and their initial positions, the optimal position strategies for the pursuer and two evaders are constructed. The formal description of the problem follows that considered in [2]. The approach proposed in [3] is developed. Similar problems were considered in [10-16]. (C) 1997 Elsevier Science Ltd. All rights reserved.