Simple pursuit problem with phase restrictions of two coordinated evaders on time scales

Abstract

In a finite-dimensional Euclidean space, the problem of a simple pursuit by a group of pursuers of two evaders is considered on a given time scale. It is assumed that all evaders use the same control and do not leave the convex polyhedral set. The pursuers use counter-strategies based on information about the initial positions and control history of the evaders. The set of admissible controls for each of the participants is a unit ball centered at zero, the target sets are the origin. The goal of the pursuers' group is the capture by two pursuers of at least one evader or the capture of two evaders. In terms of the initial positions and game parameters a sufficient capture condition has been obtained. The study uses the method of resolving functions as a basic one, which allows to obtain sufficient conditions for the solvability of the approach problem in some guaranteed time.