On the Problem of Pursuing Two Coordinated Evaders in Linear Recurrent Differential Games

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 linear nonstationary system of differential equations, under the assumption that the fundamental matrix of the homogeneous system is a recurrent function. It is assumed that the evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and the prehistory of the control of the evaders. The set of admissible controls is a strictly convex compact with a smooth boundary, and the goal sets are the origin of coordinates. The goal of the group of pursuers is the capture of at least one evader by two pursuers or the capture of two evaders. In terms of the initial positions and parameters of the game, a sufficient condition for capture is obtained. This study is based on the method of resolving functions, which makes it possible to obtain sufficient conditions for solvability of the problem of pursuit in some guaranteed time.