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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 1, Pages 54–59 (Mi vuu568)  

This article is cited in 6 scientific papers (total in 6 papers)

MATHEMATICS

One problem of group pursuit with fractional derivatives and phase constraints

N. N. Petrov

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: In the finite-dimensional Euclidean space, we consider the problem of persecution of one evader by the group of pursuers, which is described by the system
$$D^{(\alpha)}z_i = a z_i + u_i - v,$$
where $D^{(\alpha)}f$ is the Caputo derivative of order $\alpha \in (0, 1)$ of the function $f$. It is further assumed that the evader does not leave the convex polyhedron with nonempty interior. The evader uses piecewise-program strategies, and the pursuers use piecewise-program counterstrategies. The set of admissible controls is a convex compact, the target sets are the origin of coordinates, and $a$ is a real number. In terms of the initial positions and the parameters of the game, sufficient conditions for the solvability of the pursuit problem are obtained.

Keywords: differential game, group pursuit, phase restrictions, pursuer, evader.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00346_а
Ministry of Education and Science of the Russian Federation


DOI: https://doi.org/10.20537/vm170105

Full text: PDF file (239 kB)
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Bibliographic databases:

UDC: 517.977
MSC: 49N75, 91A23
Received: 01.02.2017

Citation: N. N. Petrov, “One problem of group pursuit with fractional derivatives and phase constraints”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017), 54–59

Citation in format AMSBIB
\Bibitem{Pet17}
\by N.~N.~Petrov
\paper One problem of group pursuit with fractional derivatives and phase constraints
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 1
\pages 54--59
\mathnet{http://mi.mathnet.ru/vuu568}
\crossref{https://doi.org/10.20537/vm170105}
\elib{http://elibrary.ru/item.asp?id=28808555}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Bannikov, “Uklonenie ot gruppy presledovatelei v zadache gruppovogo presledovaniya s drobnymi proizvodnymi i fazovymi ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:3 (2017), 309–314  mathnet  crossref  elib
    2. N. N. Petrov, “A multiple capture in a group pursuit problem with fractional derivatives”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S150–S157  mathnet  crossref  crossref  isi  elib
    3. A. Ya. Narmanov, K. A. Schelchkov, “Zadacha ukloneniya v nelineinoi differentsialnoi igre s diskretnym upravleniem”, Izv. IMI UdGU, 52 (2018), 75–85  mathnet  crossref  elib
    4. M. I. Gomoyunov, “Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems”, Fract. Calc. Appl. Anal., 21:5 (2018), 1238–1261  crossref  mathscinet  isi  scopus
    5. M. I. Gomoyunov, “Ekstremalnyi sdvig na soputstvuyuschie tochki v pozitsionnoi differentsialnoi igre dlya sistemy drobnogo poryadka”, Tr. IMM UrO RAN, 25, no. 1, 2019, 11–34  mathnet  crossref  elib
    6. A. I. Machtakova, “Presledovanie zhestko skoordinirovannykh ubegayuschikh v lineinoi zadache s drobnymi proizvodnymi i prostoi matritsei”, Izv. IMI UdGU, 54 (2019), 45–54  mathnet  crossref
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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