Many Pursuers and One Evader Game

In this paper we study a pursuit differential game in space Rn. The dynamic equation of finite number of pursuers and a single evader are describe by certain first order and second order differential equations respectively. The control functions (of the players) are subject to generalized coordinate-wise integral constraint. Pursuers are focused to catch the evader when the geometric position of at least one pursuer coincides with that of the evader. The pursuers’ strategies are describe in phases. Moreover, we provide conditions that ensure completion of pursuit.