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 Trudy Inst. Mat. i Mekh. UrO RAN, 2017, Volume 23, Number 1, Pages 212–218 (Mi timm1396)

A multiple capture of an evader in linear recursive differential games

N. N. Petrov, N. A. Solov'eva

Udmurt State University, Mathematical Department

Abstract: In a finite-dimensional Euclidean space, we consider a linear nonstationary problem in which one evader is pursued by a group of players and all the participants have equal capabilities. The problem is described by the system
$$\dot z_i=A(t)z_i+u_i-v,\quad z_i(t_0)=z_i^0,\quad u_i, v \in V,$$
where the set of admissible controls $V$ is a strictly convex compact set with smooth boundary. It is assumed that the fundamental matrix $\Phi(t)$ of the homogeneous system $\dot w=A(t)w$, $\Phi(t_0)=E$ is a Zubov recursive function and its derivative is uniformly bounded. The aim of the pursuing group is to capture the evader by at least $r$ different pursuers. We assume that the terminal sets are convex and compact. The pursuers use quasistrategies. We obtain sufficient conditions for the solvability of the pursuit problem in terms of the initial positions. Examples are given.

Keywords: differential game, group pursuit, recursive function.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00346 Ministry of Education and Science of the Russian Federation

DOI: https://doi.org/10.21538/0134-4889-2017-23-1-212-218

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Bibliographic databases:

UDC: 517.977
MSC: 49N75

Citation: N. N. Petrov, N. A. Solov'eva, “A multiple capture of an evader in linear recursive differential games”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 1, 2017, 212–218

Citation in format AMSBIB
\Bibitem{PetSol17} \by N.~N.~Petrov, N.~A.~Solov'eva \paper A multiple capture of an evader in linear recursive differential games \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2017 \vol 23 \issue 1 \pages 212--218 \mathnet{http://mi.mathnet.ru/timm1396} \crossref{https://doi.org/10.21538/0134-4889-2017-23-1-212-218} \elib{http://elibrary.ru/item.asp?id=28409380} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. N. Petrov, “A multiple capture in a group pursuit problem with fractional derivatives”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S150–S157
2. N. N. Petrov, A. Ya. Narmanov, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v zadache prostogo presledovaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 193–198
3. N. N. Petrov, N. A. Solov'eva, “Multiple capture of given number of evaders in linear recurrent differential games”, J. Optim. Theory Appl., 182:1, SI (2019), 417–429
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