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

TL;DR

This paper analyzes a differential game involving multiple pursuers and an evader within a convex set, focusing on pursuit completion conditions and strategy construction under integral control constraints.

Contribution

It introduces new pursuit strategies and conditions for pursuit completion in a multi-agent differential game with integral constraints on a convex set.

Findings

Pursuit can be completed under specific initial conditions.

Constructed pursuer strategies guarantee pursuit success.

Derived conditions are valid for any initial positions within the set.

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.