Asymptotically optimal feedback control for a system of linear oscillators
Alexander Ovseevich, Aleksey Fedorov
TL;DR
This paper develops an asymptotically optimal feedback control strategy for damping multiple linear oscillators with bounded control, ensuring near-minimal damping time as initial energy grows large.
Contribution
It introduces a novel feedback control method that achieves asymptotic optimality for damping linear oscillators, based on a new lemma about sustainable observability.
Findings
Control time ratio approaches 1 for large initial energy
The method guarantees asymptotic optimality in damping
New lemma on sustainable observability supports the control design
Abstract
Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the ratio of motion time to zero with this control to the minimum one is close to 1, if the initial energy of the system is large. Some of the results based on the new lemma about sustainable observability autonomous linear systems.
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