Simple Pursuit Problem with Phase Constraints of Two Coordinated Evaders on Time Scales

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

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