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Moscow Mathematical Journal, 2016, Volume 16, Number 3, Pages 561–598
DOI: https://doi.org/10.17323/1609-4514-2016-16-3-561-598 (Mi mmj609) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Asymptotic control theory for a system of linear oscillators

Aleksey Fedorovabc, Alexander Ovseevicha

a Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Vernadsky av., 101/1, Moscow, Russia
b Laboratoire de Physique Théorique et Modèles Statistiques, CNRS and Université Paris Sud, UMR8626, 91405 Orsay, France
c Russian Quantum Center, 143025 Novaya st. 100, Skolkovo, Moscow, Russia
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DOI: https://doi.org/10.17323/1609-4514-2016-16-3-561-598
Abstract: We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna–Lions theory of singular ODEs, we prove that the suggested control law correctly defines the motion of the system. The obtained control is asymptotically optimal: the ratio of the motion time to zero under this control to the minimum one is close to 1 if the initial energy of the system is large. The results are partially based on a new perturbation theory of observable linear systems.
Key words and phrases: maximum principle, reachable sets, linear systems.
Funding agency Grant number
Russian Foundation for Basic Research 11-08-00435
14-08-00606
14-01-00476
Dynasty Foundation
This work was supported by the Russian Foundation for Basic Research (grants 11-08-00435, 14-08-00606, and 14-01-00476) and the Dynasty Foundation.
Received: May 18, 2015
Bibliographic databases:
Document Type: Article
MSC: 93B03, 93B07, 93B52
Language: English
Citation: Aleksey Fedorov, Alexander Ovseevich, “Asymptotic control theory for a system of linear oscillators”, Mosc. Math. J., 16:3 (2016), 561–598
Citation in format AMSBIB
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\by Aleksey~Fedorov, Alexander~Ovseevich
\paper Asymptotic control theory for a~system of linear oscillators
\jour Mosc. Math.~J.
\yr 2016
\vol 16
\issue 3
\pages 561--598
\mathnet{http://mi.mathnet.ru/mmj609}
\crossref{https://doi.org/10.17323/1609-4514-2016-16-3-561-598}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3510212}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000391210300005}
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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