Multiple Capture of Coordinated Evaders in the Linear Group Pursuit Problemwith a Simple Matrix and Phase Restrictions

Abstract

In finite-dimensional Euclidean space, an analysis is made of the problem of pursuit of two evaders by a group of pursuers, which is described by a system of the form
$$
\dot z_{ij} = \alpha z_{ij}+ u_i - v,\ u_i, v \in V.
$$
It is assumed that the evaders use the same control and do not move out of a convex polyhedral set.
The pursuers use counterstrategies based on information about the initial positions and the prehistory of the evaders' control.
The set of admissible controls $V$  is a sphere of unit radius with its center at the origin, and the goal sets are the origin.
The goal of the group of pursuers is the capture of at least one evader by a given number of pursuers. In terms of the initial positions and parameters of the game, a sufficient condition for capture is obtained. The method of resolving functions, which is used as a basis for analysis, provides sufficient conditions for solvability of the problem of pursuit in some guaranteed time.