ABOUT ESCAPE IN GROUP DIFFERENTIAL GAME

Abstract

This article studies the problem of pursuit between a group of escapees without inertia and an inertial pursuer. In this case, the dynamic capabilities of the pursuers are superior to the capabilities of the escapees. All escapees use uniform control, in which it is assumed that the party controlling the escapees knows the position of the game participants at each moment of time and the spatial constraints imposed on the trajectory of the escapees. Here, a piecewise-invariant control is constructed that ensures that all escapees escape from a group of pursuers. A similar problem to the one studied here was studied by N.Yu. Satimov and B.B. Rikhsiev [2, 3] without spatial constraints and with one escapee. The problem of l-capturing a single escapee from a group of chasers controlled by acceleration without spatial constraints was studied by A.A. Chikriy [4], N.L. Grigorenko [1].