Geodesic
Two-time capture of coordinated evaders in a simple pursuit problem
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 2, pp. 281-292

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In a finite-dimensional Euclidean space, the problem of pursuit of two evaders by a group of pursuers described by a system of the form $$\dot z_{ij} = u_i - v,\quad u_i,v \in V,$$ is considered. It is assumed that all evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and control history of the evaders. The set of admissible controls $V$ is a unit ball centered at zero, target sets are the origin of coordinates. The goal of the pursuers' group is to capture at least one evader by two pursuers. In terms of initial positions and game parameters a sufficient condition for the capture is obtained. In the study, the method of resolving functions is used as a basic one, which allows obtaining sufficient conditions for the solvability of the approach problem in some guaranteed time.
Keywords: differential game, group pursuit, pursuer, evader. 
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     title = {Two-time capture of coordinated evaders in a simple pursuit problem},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2023_33_2_a6/}
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N. N. Petrov. Two-time capture of coordinated evaders in a simple pursuit problem. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 2, pp. 281-292. http://geodesic.mathdoc.fr/item/VUU_2023_33_2_a6/