Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin., 2024.
In finite-dimensional Euclidean space, we address the problem of a simple pursuit of two evaders by a group of pursuers in a given time scale. 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 on the initial positions and on the prehistory of the control of evaders. The set of admissible controls of each of the participants 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 two pursuers. In terms of the initial positions and parameters of the game, a sufficient condition for capture is obtained. The study is based on the method of resolving functions, which makes it possible to obtain sufficient conditions for solvability of the pursuit problem in some guaranteed time.
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