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arXiv · 1308.6090

Asymptotic control theory for a system of linear oscillators

Aleksey Fedorov·Alexander Ovseevich
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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.

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Aleksey Fedorov, Alexander Ovseevich. 2016-05-29. Asymptotic control theory for a system of linear oscillators. https://doi.org/10.17323/1609-4514-2016-16-3-561-598

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