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 Tr. Mat. Inst. Steklova, 1999, Volume 224, Pages 130–138 (Mi tm695)

To the Theory of Many-Person Differential Games

N. L. Grigorenko

Abstract: A linear differential game of a group of pursuers and one evader is considered. Sufficient conditions for the solvability of a problem of pursuit are presented in the case when it is possible to split pursuers into the following three groups of players. For the players of the first, second, and third groups, the dynamic capabilities, respectively, coincide with, exceed, and are less than the dynamic capabilities of the evader. An algorithm for finding a control of pursuing players is described. A method for calculating the guaranteed time of visiting the terminal set from a given initial position is proposed. The results of calculation of a model example are presented.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 224, 115–123

Bibliographic databases:
UDC: 517.977.1

Citation: N. L. Grigorenko, “To the Theory of Many-Person Differential Games”, Algebra. Topology. Differential equations and their applications, Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 224, Nauka, MAIK «Nauka/Inteperiodika», M., 1999, 130–138; Proc. Steklov Inst. Math., 224 (1999), 115–123

Citation in format AMSBIB
\Bibitem{Gri99} \by N.~L.~Grigorenko \paper To the Theory of Many-Person Differential Games \inbook Algebra. Topology. Differential equations and their applications \bookinfo Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin \serial Tr. Mat. Inst. Steklova \yr 1999 \vol 224 \pages 130--138 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm695} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1721358} \zmath{https://zbmath.org/?q=an:0978.91012} \transl \jour Proc. Steklov Inst. Math. \yr 1999 \vol 224 \pages 115--123