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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 1, Pages 61–70 (Mi timm1260)  

Asymptotics of the optimal time in a time-optimal control problem with a small parameter

A. R. Danilinab, O. O. Kovrizhnykhba

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: A time-optimal control problem for a singularly perturbed linear autonomous system is considered. The main difference of this case from systems with fast and slow variables studied earlier is that the eigenvalues of the matrix at the fast variables do not satisfy the standard requirement of the negativity of the real part. We obtain and justify a complete power asymptotic expansion in the sense of Erdelyi of the optimal time and optimal control with respect to the small parameter at derivatives in the equations of the system.

Keywords: optimal control, time-optimal control problem, asymptotic expansion, singularly perturbed problems, small parameter.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00322
Ministry of Education and Science of the Russian Federation 02.А03.21.0006


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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, 297, suppl. 1, 62–71

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 25.09.2015

Citation: A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal control problem with a small parameter”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 61–70; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 62–71

Citation in format AMSBIB
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