Pursuit-evasion game of many players with coordinate-wise integral constraints on a convex set in the plane

Abstract

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 x_i, i = {1, ... , m} at given time t_i (unspecified), i.e., x_i(t_i) = y(t_i). 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.