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 Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 1, Pages 147–158 (Mi timm211)

The Galilei group in an optimal control problem

I. V. Koz'min

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: In the paper, results of studying an optimal control problem for the motion of a material point under control constraints are presented. The invariance of this problem with respect to the extended Galilei group is used. From the viewpoint of calculations, the symmetry allows us to construct a family of solutions through an extremal determined numerically. From the analytical viewpoint, the symmetry gives an opportunity to reduce system's dimension and to investigate properties of extremals.

Keywords: controlled mechanical systems, symmetries

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 265, suppl. 1, S162–S173

Bibliographic databases:

UDC: 531.011

Citation: I. V. Koz'min, “The Galilei group in an optimal control problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 1, 2009, 147–158; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S162–S173

Citation in format AMSBIB
\Bibitem{Koz09} \by I.~V.~Koz'min \paper The Galilei group in an optimal control problem \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2009 \vol 15 \issue 1 \pages 147--158 \mathnet{http://mi.mathnet.ru/timm211} \elib{http://elibrary.ru/item.asp?id=11929784} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2009 \vol 265 \issue , suppl. 1 \pages S162--S173 \crossref{https://doi.org/10.1134/S0081543809060133} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000268192700013}