Differential game of many pursuers with integral constraints on a convex set in the plane

Abstract

We study a simple motion differential game of many pursuers and one evader in the plane. We give a nonempty closed convex set in the plane, and the pursuers and evader move on this set. They cannot leave this set during the game. Control functions of players are subject to coordinate-wise integral constraints. If the state of the evader $y$, coincides with that of a pursuer $x_i$, $i=\{1,...,m\}$, at some time $t_i$ (unspecified), i.e. $x_i(t_i)=y(t_i)$, then we say that pursuit is completed. We obtain some conditions under which pursuit can be completed from any position of the players in the given set. Moreover, we construct strategies for the pursuers.