Capture of two coordinated evaders in a linear pursuit problem on time scales

In a finite-dimensional Euclidean space, we consider the problem of pursuit of two evaders by a group of pursuers, described by a linear system with a simple matrix on a given time scale. It is assumed that the evaders use the same control. The pursuers employ quasistrategies based on information about the initial positions and control history of the evaders. The set of admissible controls for each participant is a ball of unit radius centered at the origin, and the terminal sets are the origin. The goal of the group of pursuers is to capture the two evaders. In the study, we use the method of resolving functions as a base one, which allows us to obtain sufficient conditions for the solvability of the approach problem in a certain guaranteed time. In terms of the initial positions and parameters of the game, a sufficient condition for capturing the evaders is obtained.