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 Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 1, Pages 71–80 (Mi timm1143)

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

A. R. Danilinab, O. O. Kovrizhnykhab

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 system for fast variables is not asymptotically stable. Asymptotic expansions of the optimal time and optimal control with respect to the small parameter at derivatives in the equations of the system are constructed.

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

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Bibliographic databases:
UDC: 517.977

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, 21, no. 1, 2015, 71–80

Citation in format AMSBIB
\Bibitem{DanKov15} \by A.~R.~Danilin, O.~O.~Kovrizhnykh \paper Asymptotics of the optimal time in a time-optimal control problem with a small parameter \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2015 \vol 21 \issue 1 \pages 71--80 \mathnet{http://mi.mathnet.ru/timm1143} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3379604} \elib{https://elibrary.ru/item.asp?id=23137973}