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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 2, Pages 193–198 (Mi vuu630)  

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

MATHEMATICS

Multiple capture of a given number of evaders in the problem of a simple pursuit

N. N. Petrova, A. Ya. Narmanovb

a Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
b National University of Uzbekistan, ul. Universitetskaya, 4, Tashkent, 100174, Uzbekistan

Abstract: In the finite-dimensional Euclidean space, the problem of a group of pursuers pursuing a group of evaders is considered, which is described by the system
$$\dot z_{ij} = u_i - v_j,\quad u_i, v_j \in V.$$
The set of admissible controls is a convex compact, and the target's sets are the origin of coordinates. The aim of the group of pursuers is to carry out an $r$-fold capture of at least $q$ evaders. Additionally, it is assumed that the evaders use program strategies and that each pursuer can catch no more than one evader. We obtain necessary and sufficient conditions for the solvability of the pursuit problem. For the proof we use the Hall theorem on the system of various representatives.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 18-51-41005_Узб_т


DOI: https://doi.org/10.20537/vm180205

Full text: PDF file (216 kB)
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Bibliographic databases:

UDC: 517.977
MSC: 49N75, 91A23
Received: 03.06.2018

Citation: N. N. Petrov, A. Ya. Narmanov, “Multiple capture of a given number of evaders in the problem of a simple pursuit”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:2 (2018), 193–198

Citation in format AMSBIB
\Bibitem{PetNar18}
\by N.~N.~Petrov, A.~Ya.~Narmanov
\paper Multiple capture of a given number of evaders in the problem of a simple pursuit
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 2
\pages 193--198
\mathnet{http://mi.mathnet.ru/vuu630}
\crossref{https://doi.org/10.20537/vm180205}
\elib{http://elibrary.ru/item.asp?id=35258686}


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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
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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