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Trudy Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 1, Pages 156–164 (Mi timm1504)  

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

A multiple capture in a group pursuit problem with fractional derivatives

N. N. Petrov

Udmurt State University, Mathematical Department

Abstract: In a finite-dimensional Euclidean space, we consider a problem of pursuing one evader by a group of pursuers with equal capabilities of all participants. The dynamics of the problem is described by the system
$$ D^{(\alpha)}z_i=az_i+u_i-v,\quad u_i,v\in V, $$
where $D^{(\alpha)}f$ is the Caputo derivative of order $\alpha\in(1,2)$ of the function $f$. The set of admissible controls $V$ is a strictly convex compact set and $a$ is a real number. The aim of the group of pursuers is to catch the evader by at least $m$ different pursuers, possibly at different times. The terminal sets are the origin. The pursuers use quasi-strategies. We obtain sufficient conditions for the solvability of the pursuit problem in terms of the initial positions. The investigation is based on the method of resolving functions, which allows us to obtain sufficient conditions for the termination of the approach problem in some guaranteed time.

Keywords: differential game, group pursuit, multiple capture, pursuer, evader.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00346
Ministry of Education and Science of the Russian Federation 1.5211.2017/8.9


DOI: https://doi.org/10.21538/0134-4889-2018-24-1-156-164

Full text: PDF file (187 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2019, 305, suppl. 1, S150–S157

Bibliographic databases:

UDC: 517.977
MSC: 49N75, 49N70, 91A24
Received: 25.09.2017

Citation: N. N. Petrov, “A multiple capture in a group pursuit problem with fractional derivatives”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 1, 2018, 156–164; Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S150–S157

Citation in format AMSBIB
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\by N.~N.~Petrov
\paper A multiple capture in a group pursuit problem with fractional derivatives
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 1
\pages 156--164
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\elib{http://elibrary.ru/item.asp?id=32604052}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2019
\vol 305
\issue , suppl. 1
\pages S150--S157
\crossref{https://doi.org/10.1134/S0081543819040151}
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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. N. N. Petrov, A. Ya. Narmanov, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v zadache s drobnymi proizvodnymi i prostoi matritsei”, Tr. IMM UrO RAN, 25, no. 3, 2019, 188–199  mathnet  crossref  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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