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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 3, Pages 104–112 (Mi timm967)  
This article is cited in 3 scientific papers (total in 3 papers)

Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints

A. R. Danilinab, N. S. Korobitsynab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after B. N. Yeltsin
Full-text PDF (175 kB) Citations (3)
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Abstract: An optimal control problem is considered for solutions of a boundary value problem for a second-order ordinary differential equation on a closed interval with a small parameter at the second derivative. The control is scalar and satisfies geometric constraints. General theorems on approximation are obtained. Two leading terms of an asymptotic expansion of the solution are constructed and an error estimate is obtained for these approximations.
Keywords: optimal control, time-optimal problem, asymptotic expansion, singular perturbation problems, small parameter.
Received: 21.03.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 285, Issue 1, Pages S58–S67
DOI: https://doi.org/10.1134/S008154381405006X
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. R. Danilin, N. S. Korobitsyna, “Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 104–112; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S58–S67
Citation in format AMSBIB
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\paper Asymptotic estimates for a~solution of a~singular perturbation optimal control problem on a~closed interval under geometric constraints
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\pages 104--112
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  • https://www.mathnet.ru/eng/timm967
  • https://www.mathnet.ru/eng/timm/v19/i3/p104
    • This publication is cited in the following 3 articles:
    1. Nguyen Thi Hoai, “Asymptotic approximation to a solution of a singularly perturbed linear-quadratic optimal control problem with second-order linear ordinary differential equation of state variable”, NACO, 11:4 (2021), 495  crossref
    2. A. R. Danilin, “A complete asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with geometric constraints”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 119–127  mathnet  crossref  mathscinet  isi  elib
    3. A. R. Danilin, “Asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with integral constraint”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 66–76  mathnet  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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