On two differential games of simple group pursuit
Two differential games of the simple pursuit of a group of evaders by a group of pursuers are considered. The first problem is devoted to the pursuit of a group of rigidly co-ordinated evaders by a group of pursuers with equal possibilities for all participants. It is supposed that the evaders remain in the bounds of the convex polyhedral set, terminal sets are convex compacts and the aim of the group of pursuers is to capture at least one evader. The solvability conditions of the problem of pursuit and the problem of evasion are obtained in the terms of initial positions and parameters of the game. The second problem is devoted to the pursuit of a group of evaders by a group of pursuers under condition that the evaders use program strategies and one pursuer can catch only one evader. The aim of a group of pursuers is to capture a specified number of evaders. Terminal sets are convex compacts, the set of possible controls is an arbitrary convex compact. Necessary and sufficient solvability conditions of the problem of pursuit are obtained.