This article is cited 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.

UDC: 517.977.8+519.837.4

MSC: 49N70, 49N75

Received: 20.02.2016

DOI: 10.20537/vm160104

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