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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1, Pages 92–99 (Mi timm1032)  

This article is cited in 2 scientific papers (total in 2 papers)

Asymptotics of the optimal time in a time-optimal problem with two small parameters

A. R. Danilinab, O. O. Kovrizhnykhab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after the First President of Russia B. N. Yeltsin

Abstract: A time-optimal problem of control of a small-mass point by a force of bounded magnitude in a nonresisting medium is considered. An asymptotic expansion of the optimal time and optimal control is constructed with respect to two independent small parameters: the mass of the point and the perturbation of the initial conditions. It is shown that the asymptotics of the optimal time in this problem is complicated even for cases of general position.

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

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 288, suppl. 1, 46–53

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 08.09.2013

Citation: A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal problem with two small parameters”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 92–99; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 46–53

Citation in format AMSBIB
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\paper Asymptotics of the optimal time in a~time-optimal problem with two small parameters
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\vol 20
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\pages 92--99
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\jour Proc. Steklov Inst. Math. (Suppl.)
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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. 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
    2. 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
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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