The linear problem of pursuing one evader by a group of pursuers is considered in a finite-dimensional Euclidean space. In a given timescale, the problem is described by a linear system with a simple matrix. The set of admissible controls for each participant is the unit ball centered at the origin. The terminal sets are given convex compact sets. The pursuers use counter-strategies based on information about the initial positions and control history of the evader. Sufficient conditions for the capture of the evader by a given number of pursuers are obtained in terms of the initial positions and parameters of the game. Sufficient evasion conditions are obtained for discrete time scales.
Keywords: differential game, group pursuit, evader, pursuer, multiple capture, timescale
Received March 12, 2024
Revised May 15, 2024
Accepted May 20, 2024
Funding Agency: This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project no. FEWS-2024-0009).
Elena Sergeevna Mozhegova, doctoral student, Udmurt State University, Izhevsk, 426034 Russia, e-mail: mozhegovalena@yandex.ru
Nikolai Nikandrovich Petrov, Dr. Phys.-Math. Sci., Prof., Udmurt State University, Izhevsk, 426034, Russia, e-mail: kma3@list.ru
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Cite this article as: E.S. Mozhegova, N.N. Petrov. Multiple capture of an evader in the linear pursuit problem on timescales. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 3, pp. 217–228.
