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Izv. IMI UdGU, 2019, Volume 54, Pages 45–54 (Mi iimi381)  

This article is cited in 2 scientific papers (total in 2 papers)

Persecution of rigidly coordinated evaders in a linear problem with fractional derivatives and a simple matrix

A. I. Machtakova

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

Abstract: In the finite-dimensional Euclidean space, the problem of pursuit of a group of evaders by a group of pursuers is considered, which is described by a system of the form
$$D^{(\alpha)} z_{ij} = a z_{ij} + u_i - v,$$
where $D^{(\alpha)} f$ is the Caputo derivative of the order $\alpha \in (0,1)$ of the function $f$. It is assumed that all evaders use the same control. The goal of the pursuers is to catch at least one of the evaders. The evaders use piecewise-program strategies, and the pursuers use piecewise-program counterstrategies. Every pursuer catches not more than one evader. The set of admissible controls is a ball of unit radius with the center at the origin, the target sets are the origin. In terms of initial positions and game parameters, a sufficient conditions for the capture are obtained.

Keywords: differential game, group persecution, pursuer, evader, fractional derivatives.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-51-41005_Узб_т
This work was funded by RFBR, project number 18–51–41005.


DOI: https://doi.org/10.20537/2226-3594-2019-54-04

Full text: PDF file (139 kB)
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Bibliographic databases:

UDC: 517.977
MSC: 91A23, 49N70
Received: 15.08.2019

Citation: A. I. Machtakova, “Persecution of rigidly coordinated evaders in a linear problem with fractional derivatives and a simple matrix”, Izv. IMI UdGU, 54 (2019), 45–54

Citation in format AMSBIB
\Bibitem{Mac19}
\by A.~I.~Machtakova
\paper Persecution of rigidly coordinated evaders in a linear problem with fractional derivatives and a simple matrix
\jour Izv. IMI UdGU
\yr 2019
\vol 54
\pages 45--54
\mathnet{http://mi.mathnet.ru/iimi381}
\crossref{https://doi.org/10.20537/2226-3594-2019-54-04}
\elib{https://elibrary.ru/item.asp?id=41435140}


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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. I. Machtakova, “Poimka dvukh skoordinirovannykh ubegayuschikh v zadache s drobnymi proizvodnymi, fazovymi ogranicheniyami i prostoi matritsei”, Izv. IMI UdGU, 56 (2020), 50–62  mathnet  crossref
    2. N. N. Petrov, “Ob odnoi zadache presledovaniya gruppy ubegayuschikh vo vremennykh shkalakh”, Tr. IMM UrO RAN, 27, no. 3, 2021, 163–171  mathnet  crossref  elib
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