PURSUIT-EVASION GAME OF MANY PLAYERS WITH COORDINATE-WISE INTEGRAL CONSTRAINTS ON A CONVEX SET IN THE PLANE

We study a differential game of many pursuers and one evader in the plane. It is assumed that the pursuers and evader move is allowed within a non empty closed convex set in the plane. Control functions of players are subject to coordinate-wise integral constraints. The game is over when the state of the evader y coincides with that of a pursuer xi, i = {1,..., m} at given time ti (unspecified), i.e., xi(ti) = y(ti). We obtain conditions under which the game is over in finite time, no matter where the players start from. Moreover, we construct winning for the pursuers.