A differential game of pursuit for an infinite system of simple motion in the plane

Abstract

In the present paper, we investigate a differential game of pursuit for an infinite system of simple motion in a plane. The control functions of the players satisfies both geometric and integral constraints respectively. In the plane, the game is assume to be completed if the state of the pursuer xk, k = 1, 2, ... is directly coincide with that of the evader yk, k = 1, 2, ..., i.e; xk(x ) = yk(x ), k = 1,2, ..., at some time x and the evader is tries to stop the incident. In addition to that the strategy of the pursuer with respect to geometric and integral constraints will be constructed. Moreover, a numerical example will be given to illustrate the result.