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Russia Izhevsk; Yekaterinburg
Year
2022
Volume
32
Issue
1
Pages
94-106
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Section Mathematics
Title Group pursuit in a problem with fractional derivatives in the class of positional strategies with a guide
Author(-s) Petrov N.N.ab, Machtakova A.I.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Udmurt State Universityb
Abstract In a finite-dimensional Euclidean space, the problem of pursuing one evader by a group of pursuers is considered, described by a system of the form $$D^{(\alpha)} z_i = a_i z_i + u_i - v,\quad u_i, v \in V,$$ where $D^{(\alpha)}f$ is the Caputo derivative of order $\alpha\in(0,1)$ of the function $f$. The set of admissible controls $V$ is a convex compact, $a_i$ are non-positive real numbers. The aim of the group of pursuers is to capture the evader. The terminal sets are the origin of coordinates. Sufficient conditions for catching one evader in the class of quasi-strategies are obtained. Using quasi-strategies in an auxiliary game, sufficient conditions for catching an evader in the class of positional strategies with a guide are obtained.
Keywords differential game, group pursuit, pursuer, evader, guide system
UDC 517.977
MSC 49N79, 49N70, 91A24
DOI 10.35634/vm220107
Received 2 October 2021
Language Russian
Citation Petrov N.N., Machtakova A.I. Group pursuit in a problem with fractional derivatives in the class of positional strategies with a guide, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 1, pp. 94-106.
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