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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 67–79 (Mi timm809)  

This article is cited in 4 scientific papers (total in 4 papers)

Asymptotic representation of a solution to a singular perturbation linear time-optimal problem

A. R. Danilinab, O. O. Kovrizhnykhab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University

Abstract: A time-optimal control problem is considered for a linear system with fast and slow variables and smooth geometric constraints on the control. An asymptotic expansion of the optimal time up to the second order of smallness is constructed and validated.

Keywords: optimal control, time-optimal control problem, asymptotic expansion, singular perturbation problems, small parameter.

Full text: PDF file (207 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 281, suppl. 1, 22–35

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 20.12.2011

Citation: A. R. Danilin, O. O. Kovrizhnykh, “Asymptotic representation of a solution to a singular perturbation linear time-optimal problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 67–79; Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 22–35

Citation in format AMSBIB
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\paper Asymptotic representation of a~solution to a~singular perturbation linear time-optimal problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 18
\issue 2
\pages 67--79
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
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\vol 281
\issue , suppl. 1
\pages 22--35
\crossref{https://doi.org/10.1134/S0081543813050039}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Danilin A.R., Kovrizhnykh O.O., “Time-Optimal Control of a Small MASS Point Without Environmental Resistance”, Dokl. Math., 88:1 (2013), 465–467  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal problem with two small parameters”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 46–53  mathnet  crossref  mathscinet  isi  elib
    3. A. R. Danilin, O. O. Kovrizhnykh, “Asimptotika optimalnogo vremeni v odnoi zadache o bystrodeistvii s malym parametrom”, Tr. IMM UrO RAN, 21, no. 1, 2015, 71–80  mathnet  mathscinet  elib
    4. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal control problem with a small parameter”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 62–71  mathnet  crossref  mathscinet  isi  elib
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