CONSTRUCTION OF THE VALUE FUNCTION IN A GAME OF APPROACH WITH SEVERALPURSUERS

A differential game of approach of one evader with n dynamic pursuers is investigated. All the players have simple motions. The velocities o f the players and the time of the game are limited. The case of a game with both similar arbitrary pursuers and pursuers of different types whose velocities exceed that of the evader are considered. The payoff is taken to be the distance between the evader and the closest pursuer at the instant when the game terminates. The formalization used is th e same as that employed in [1, 2]. The method used in [3, 4] of solvin g problems of the approach of two pursuers with a single evader in a p lane is extended to the solution of the problem of the approach of n p ursuers with a single evader in space R. The value function of the gam e is constructed not only in a regular region [5], but also in a separ ate singular manifold. A programmed maximin function is introduced, th e space of the initial positions is decomposed into regions, and the u -stability of the function over the whole of the space is proved. An e xample of a game of pursuit of ''three after one'' in a three-dimensio nal Euclidean space is given, and the optimal trajectories and the lev el surfaces of the value of the game are constructed.