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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2014 Volume 20, Number 3, Pages 76–85 (Mi timm1086)

This article is cited 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

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.

UDC: 517.977

Received: 16.04.2014


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2015, 291, suppl. 1, S66–S76

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