On one simple pursuit problem of two rigidly coordinated evaders

Abstract

In a finite-dimensional Euclidean space, the problem of pursuit by a group of pursuers of two evaders described by a system of the form $$\dot z_{ij} = u_i - v,\quad u_i, v \in V $$ is considered. It is assumed that all evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and control history of the evaders. The set of admissible controls $V$ is unit ball centered at zero, target sets are the origin. The goal of the pursuers' group is to capture at least one evader by two pursuers or to capture two evaders. In terms of initial positions and game parameters a sufficient condition for the capture is obtained. In the study, the method of resolving functions is used as a basic one, which allows obtaining sufficient conditions for the solvability of the approach problem in some guaranteed time.