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 Trudy Inst. Mat. i Mekh. 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

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.À03.21.0006

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, 296, suppl. 1, 119–127

Bibliographic databases:

UDC: 517.977

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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