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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2020, Volume 30, Issue 1, Pages 64–91 (Mi vuu711)  

MATHEMATICS

Relaxation of pursuit-evasion differential game and program absorption operator

A. G. Chentsovab, D. M. Khachaia

a N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia

Abstract: We consider some natural relaxation of pursuit-evasion differential game. For two closed sets, which are parameters, similar guidance problem for $\varepsilon$-neighborhoods is being solved. We are interested in finding a minimal size of such neighborhoods, which allows player I successfully solve his guidance problem in the class of generalized non-anticipating strategies. To resolve above-mentioned differential game, a modification of Program Iterations Method is implemented. Size of the neighborhoods is found as a position function and it's defined by application of special iterative procedure further below. As a corollary, it is shown that desired function is a fixed point of the open-loop operator, which defines the procedure.

Keywords: pursuit-evasion differential game, program iterations method, guaranteed result.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-000573_а
The study was funded by RFBR, project number 19-01-000573 A.


DOI: https://doi.org/10.35634/vm200106

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Full text: http://vm.udsu.ru/.../2020-1-6
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Bibliographic databases:

UDC: 519.6
MSC: 05A05, 97N70, 97N80
Received: 02.01.2020

Citation: A. G. Chentsov, D. M. Khachai, “Relaxation of pursuit-evasion differential game and program absorption operator”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:1 (2020), 64–91

Citation in format AMSBIB
\Bibitem{CheKha20}
\by A.~G.~Chentsov, D.~M.~Khachai
\paper Relaxation of pursuit-evasion differential game and program absorption operator
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 1
\pages 64--91
\mathnet{http://mi.mathnet.ru/vuu711}
\crossref{https://doi.org/10.35634/vm200106}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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