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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 3, Pages 76–85 (Mi timm1086)  
This article is cited in 3 scientific papers (total in 3 papers)

Asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with integral constraint

A. R. Danilinab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University
Full-text PDF (176 kB) Citations (3)
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Abstract: A control problem for solutions of a boundary value problem for a second-order ordinary differential equation with a small parameter at the second derivative is considered on a closed interval. The control is scalar and subject to integral constraints. We construct a complete asymptotic expansion in powers of the small parameter in the Erdelyi sense.
Keywords: optimal control, time-optimal problem, asymptotic expansion, singular perturbation problems, small parameter.
Received: 16.04.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 291, Issue 1, Pages 66–76
DOI: https://doi.org/10.1134/S0081543815090059
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. R. Danilin, “Asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with integral constraint”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 76–85; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 66–76
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/timm1086
  • https://www.mathnet.ru/eng/timm/v20/i3/p76
    • This publication is cited in the following 3 articles:
    1. Thi Hoai Nguyen, “Asymptotic Solution of a Singularly Perturbed Optimal Problem with Integral Constraint”, J Optim Theory Appl, 190:3 (2021), 931  crossref
    2. 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
    3. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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