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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 1, Pages 63–75 (Mi timm529)  

This article is cited in 6 scientific papers (total in 6 papers)

Asymptotics of the optimal time in a singular perturbation linear problem

A. R. Danilin, O. O. Kovrizhnykh

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

Abstract: A time-optimal control problem is considered for a linear system with fast and slow variables and smooth geometric constraints on the control. For the optimal time and optimal control, asymptotic expansions in a small parameter at the derivatives in the equations of the system and a small perturbation of the initial conditions are constructed.

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

Full text: PDF file (191 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 271, suppl. 1, S53–S65

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 11.11.2009

Citation: A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a singular perturbation linear problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 63–75; Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S53–S65

Citation in format AMSBIB
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\paper Asymptotics of the optimal time in a~singular perturbation linear problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\pages 63--75
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\issue , suppl. 1
\pages S53--S65
\crossref{https://doi.org/10.1134/S0081543810070059}
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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., “O zavisimosti zadachi bystrodeistviya dlya lineinoi sistemy ot dvukh malykh parametrov”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 27, 46–60  mathscinet  elib
    2. A. R. Danilin, O. O. Kovrizhnykh, “O zavisimosti zadachi bystrodeistviya dlya lineinoi sistemy ot dvukh malykh parametrov”, Vestnik ChelGU, 2011, no. 14, 46–60  mathnet
    3. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotic representation of a solution to a singular perturbation linear time-optimal problem”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 22–35  mathnet  crossref  isi  elib
    4. A. I. Korotkii, N. A. Artemova, N. A. Vaganova, O. O. Kovrizhnykh, L. I. Rubina, O. N. Ulyanov, O. V. Ushakova, M. Yu. Filimonov, I. A. Tsepelev, “O razrabotkakh analiticheskikh i chislennykh metodov resheniya zadach mekhaniki sploshnoi sredy”, Tr. IMM UrO RAN, 19, no. 2, 2013, 203–215  mathnet  mathscinet  elib
    5. 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
    6. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of a solution to a singularly perturbed time-optimal control problem”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 60–69  mathnet  crossref  crossref  isi  elib
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