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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, Volume 26, Issue 1, Pages 46–57
DOI: https://doi.org/10.20537/vm160104
(Mi vuu517)
 

This article is cited in 11 scientific papers (total in 11 papers)

MATHEMATICS

Multiple capture of rigidly coordinated evaders

A. I. Blagodatskikh

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
References:
Abstract: The present paper deals with the problem of pursuit of a group of rigidly coordinated evaders in a nonstationary conflict-controlled process with equal opportunities
$$
\begin{array}{llllllllcccc} P_i&:&\dot x_i=A(t)x_i+u_i,& u_i\in U(t),& x_i(t_0)=X_i^0,& i=1,2,\dots,n,\\ E_j&:&\dot y_j=A(t)y_j+v,& v\in U(t),& y_j(t_0)=Y_j^0,& j=1,2,\dots,m.\\ \end{array}
$$
We say that a multiple capture in the problem of pursuit holds if the specified number of pursuers catch evaders, possibly at different times
$$ x_\alpha(\tau_\alpha)=y_{j_\alpha}(\tau_\alpha),\quad\alpha\in\Lambda,\quad\Lambda\subset\{1,2,\dots,n\},\quad|\Lambda|=b\quad(n\geqslant b\geqslant 1),\quad j_\alpha\subset\{1,2,\dots,m\}. $$
The problem of nonstrict simultaneous multiple capture requires that capture moments coincide
$$ x_\alpha (\tau)=y_{j_\alpha}(\tau),\quad\alpha\in\Lambda. $$
The problem of a simultaneous multiple capture requires that lowest capture moments coincide
$$ x_\alpha(\tau)=y_{j_\alpha}(\tau),\quad x_\alpha(s)\ne y_{j_\alpha}(s),\quad s\in[t_0, \tau),\quad\alpha\in\Lambda. $$
In this paper we obtain necessary and sufficient conditions for simultaneous multiple capture and nonstrict simultaneous multiple capture.
Keywords: capture, multiple capture, simultaneous multiple capture, pursuit, evasion, differential games, conflict-controlled processes.
Received: 20.02.2016
Bibliographic databases:
Document Type: Article
UDC: 517.977.8+519.837.4
MSC: 49N70, 49N75
Language: Russian
Citation: A. I. Blagodatskikh, “Multiple capture of rigidly coordinated evaders”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016), 46–57
Citation in format AMSBIB
\Bibitem{Bla16}
\by A.~I.~Blagodatskikh
\paper Multiple capture of rigidly coordinated evaders
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2016
\vol 26
\issue 1
\pages 46--57
\mathnet{http://mi.mathnet.ru/vuu517}
\crossref{https://doi.org/10.20537/vm160104}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3485572}
\elib{https://elibrary.ru/item.asp?id=25681784}
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  • https://www.mathnet.ru/eng/vuu517
  • https://www.mathnet.ru/eng/vuu/v26/i1/p46
  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    References:71
     
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