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Trudy Inst. Mat. i Mekh. UrO RAN, 2007, Volume 13, Number 2, Pages 55–65 (Mi timm88)  

This article is cited in 3 scientific papers (total in 3 papers)

The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case

A. R. Danilin, Yu. V. Parysheva


Abstract: An optimal control problem is investigated for a linear system with fast and slow variables, a convex terminal performance functional depending on the slow variables, and smooth geometric constraints on the control. Sufficient regularity conditions are presented for the asymptotics of a solution of this problem, and a complete asymptotic expansion of the optimal value of the performance functional in powers of a small parameter is constructed.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2007, 259, suppl. 2, S83–S94

Document Type: Article
UDC: 517.977
Received: 12.03.2007

Citation: A. R. Danilin, Yu. V. Parysheva, “The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 2, 2007, 55–65; Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S83–S94

Citation in format AMSBIB
\Bibitem{DanPar07}
\by A.~R.~Danilin, Yu.~V.~Parysheva
\paper The asymptotics of the optimal value of the performance functional in a~linear optimal control problem in the regular case
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2007
\vol 13
\issue 2
\pages 55--65
\mathnet{http://mi.mathnet.ru/timm88}
\elib{http://elibrary.ru/item.asp?id=12040768}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2007
\vol 259
\issue , suppl. 2
\pages S83--S94
\crossref{https://doi.org/10.1134/S0081543807060053}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Danilin A.R., Parysheva Yu.V., “Asymptotics of the optimal cost functional in a linear optimal control problem”, Dokl. Math., 80:1 (2009), 478–481  crossref  mathscinet  zmath  isi  elib  scopus
    2. Yu. V. Parysheva, “Asimptotika optimalnogo upravleniya v zadache minimizatsii terminalnogo funktsionala na traektoriyakh sistemy s bystrymi i medlennymi peremennymi”, Tr. IMM UrO RAN, 16, no. 2, 2010, 186–198  mathnet  elib
    3. “On the asymptotics of the optimal value of the performance functional in a linear optimal control problem”, Differ. Equ., 47:4 (2011), 560–570  crossref  mathscinet  zmath  isi  elib  elib  scopus
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