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JOURNALS // Moscow Mathematical Journal // Archive

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

This article is cited 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

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.

MSC: 93B03, 93B07, 93B52

Received: May 18, 2015

Language: English

DOI: 10.17323/1609-4514-2016-16-3-561-598



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