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Mosc. Math. J., 2016, Volume 16, Number 3, Pages 561–598 (Mi mmj609)  

This article is cited in 4 scientific papers (total in 4 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

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.


DOI: https://doi.org/10.17323/1609-4514-2016-16-3-561-598

Full text: http://www.mathjournals.org/.../2016-016-003-005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 93B03, 93B07, 93B52
Received: May 18, 2015
Language:

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
\Bibitem{FedOvs16}
\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://www.ams.org/mathscinet-getitem?mr=3510212}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000391210300005}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Ovseevich, A. K. Fedorov, “Asymptotically optimal control for a simplest distributed system”, Dokl. Math., 95:2 (2017), 194–197  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. A. K. Fedorov, A. I. Ovseevich, “Asymptotic control theory for a closed string”, Russ. J. Math. Phys., 25:2 (2018), 200–219  crossref  mathscinet  zmath  isi  scopus
    3. A. Fedorov, A. Ovseevich, “Asymptotically optimal dry-friction like control for a simplest distributed system”, IFAC-PapersOnLine, 51:32 (2018), 87–92  crossref  isi  scopus
    4. A. A. Galyaev, P. V. Lysenko, “Energy-optimal control of harmonic oscillator”, Autom. Remote Control, 80:1 (2019), 16–29  mathnet  crossref  crossref  isi  elib
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