Some methods of pursuit in linear discrete games with integral constraints (Q913678)

A linear discrete game of pursuit of one evader by several pursuers with integral constraints on the controls is considered. The dynamics of the game is given by a system of difference equations with constant coefficients. The aim of the evader is to prevent the trajectory of the game from hitting the terminal sets \(M_ 1,...,M_ m\), where m is the number of pursuers. One says that the game can be completed in the k-th step if for each strategy of the evader there exists a strategy of pursuit guaranteeing that at least one pursuer hits his terminal set in this step. Sufficient conditions for the completion of the game are presented. An efficient construction method for the pursuit strategy is found. The cases of (1) one pursuer and (2) complete information are studied more explicitely. It must be mentioned that the assumptions on information of the pursuers is of a very general kind that includes the cases of complete and incomplete information as well as the case of information with time lag.