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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 1, Pages 52–60 (Mi timm1259)  
A complete asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with geometric constraints

A. R. Danilinab

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
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Abstract: We consider an optimal control problem for solutions of a boundary value problem on an interval for a second-order ordinary differential equation with a small parameter at the second derivative. The control is scalar and satisfies geometric constraints. Expansions of a solution to this problem up to any power of the small parameter are constructed and validated.
Keywords: optimal control, asymptotic expansion, singular perturbation problems, small parameter.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00322
Ural Branch of the Russian Academy of Sciences
Ministry of Education and Science of the Russian Federation 02.А03.21.0006
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 296, Issue 1, Pages 119–127
DOI: https://doi.org/10.1134/S0081543817020110
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. R. Danilin, “A complete asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with geometric constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 52–60; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 119–127
Citation in format AMSBIB
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\paper A complete asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with geometric constraints
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\pages 52--60
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages 119--127
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