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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 1, Pages 92–99 (Mi timm1032)  
This article is cited in 3 scientific papers (total in 3 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
Full-text PDF (161 kB) Citations (3)
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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.
Received: 08.09.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 288, Issue 1, Pages 46–53
DOI: https://doi.org/10.1134/S0081543815020066
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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