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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
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
Citation:
A. I. Blagodatskikh, “Multiple capture of rigidly coordinated evaders”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016), 46–57
Linking options:
https://www.mathnet.ru/eng/vuu517 https://www.mathnet.ru/eng/vuu/v26/i1/p46
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