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 Tr. Mat. Inst. Steklova, 2012, Volume 277, Pages 49–56 (Mi tm3377)

Game problem of controlling three dynamical systems with fixed final times

N. L. Grigorenko

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

Abstract: A three-player game is considered in which the first and second players have dynamic superiority over the third player. Two fixed time points are specified. The game ends if either the first player captures the third player at the first time point, or the second player captures the third player at the second time point. We analyze a situation when the initial positions in the game are such that neither the first nor the second player alone can capture the third player at the specified points of time. We propose sufficient conditions on the parameters of the game under which, for given initial states of the players, the first and second players by applying some controls can guarantee that one of them will meet the third player at the prescribed moment. Simulation results for a model example are also presented.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 277, 43–50

Bibliographic databases:

UDC: 517.978
Received in February 2012

Citation: N. L. Grigorenko, “Game problem of controlling three dynamical systems with fixed final times”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Tr. Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 49–56; Proc. Steklov Inst. Math., 277 (2012), 43–50

Citation in format AMSBIB
\Bibitem{Gri12} \by N.~L.~Grigorenko \paper Game problem of controlling three dynamical systems with fixed final times \inbook Mathematical control theory and differential equations \bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko \serial Tr. Mat. Inst. Steklova \yr 2012 \vol 277 \pages 49--56 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3377} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3052263} \elib{https://elibrary.ru/item.asp?id=17759397} \transl \jour Proc. Steklov Inst. Math. \yr 2012 \vol 277 \pages 43--50 \crossref{https://doi.org/10.1134/S0081543812040049} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309232900004} \elib{https://elibrary.ru/item.asp?id=23960346} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904061127} 

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