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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2024, Volume 34, Issue 1, Pages 65–79
DOI: https://doi.org/10.35634/vm240105
(Mi vuu879)
 

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On two problems of pursuit of a group of evaders in differential games with fractional derivatives

A. I. Machtakovaab, N. N. Petrovab

a Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620108, Russia
Full-text PDF (223 kB) Citations (1)
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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
Funding agency Grant number
Russian Science Foundation 21–71–10070
This work was supported by the Russian Science Foundation, project 21–71–10070, https://rscf.ru/en/project/21-71-10070/.
Received: 10.01.2024
Accepted: 20.02.2024
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 49N70, 91A24
Language: Russian
Citation: A. I. Machtakova, N. N. Petrov, “On two problems of pursuit of a group of evaders in differential games with fractional derivatives”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 34:1 (2024), 65–79
Citation in format AMSBIB
\Bibitem{MacPet24}
\by A.~I.~Machtakova, N.~N.~Petrov
\paper On two problems of pursuit of a group of evaders in differential games with fractional derivatives
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2024
\vol 34
\issue 1
\pages 65--79
\mathnet{http://mi.mathnet.ru/vuu879}
\crossref{https://doi.org/10.35634/vm240105}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    Abstract page:118
    Full-text PDF :72
    References:21
     
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