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Russia Izhevsk; Yekaterinburg
Year
2024
Volume
34
Issue
1
Pages
65-79
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Section Mathematics
Title On two problems of pursuit of a group of evaders in differential games with fractional derivatives
Author(-s) Machtakova A.I.ab, Petrov N.N.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 pursuit of a group of evaders by a group of pursuers is considered, described by a system of the form \begin{gather*} D^{(\alpha)}x_i = a_i x_i + u_i, \ u_i \in U_i, \quad D^{(\alpha)}y_j = b_jy_j + v, \ v\in V, \end{gather*} where $D^{(\alpha)}f$ is the Caputo derivative of order $\alpha$ of the function $f$. The sets of admissible controls $U_i, V$ are convex compacts, $a_i, b_j$ are real numbers. The terminal sets are convex compacts. Sufficient conditions for the solvability of the pursuit problems are obtained. In the study, the method of resolving functions is used as the basic one. It is shown that such a conflict situation with equal opportunities for all participants is possible, in which one pursuer catches all the evaders.
Keywords differential game, group pursuit, pursuer, evader, fractional derivative
UDC 517.977
MSC 49N70, 91A24
DOI 10.35634/vm240105
Received 10 January 2024
Language Russian
Citation Machtakova A.I., Petrov N.N. On two problems of pursuit of a group of evaders in differential games with fractional derivatives, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2024, vol. 34, issue 1, pp. 65-79.
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