Asymptotic control theory for a system of linear oscillators
Optimization and Control
2019-10-10 v3
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.
Keywords
Cite
@article{arxiv.1308.6090,
title = {Asymptotic control theory for a system of linear oscillators},
author = {Aleksey Fedorov and Alexander Ovseevich},
journal= {arXiv preprint arXiv:1308.6090},
year = {2019}
}
Comments
34 pages; published version