Asymptotically optimal control for a simplest distributed system
Optimization and Control
2017-05-19 v2 Analysis of PDEs
Dynamical Systems
Abstract
We study the problem of the minimum-time damping of a closed string under a bounded load, applied at a single fixed point. A constructive feedback control law is designed, which allows bringing the system to a bounded neighbourhood of the terminal manifold. The law has the form of the dry friction at the point, where the load is applied. The motion under the control is governed by a nonlinear wave equation. The existence and uniqueness of solution of the Cauchy problem for this equation are proved. The main result is the asymptotic optimality of the suggested control law.
Cite
@article{arxiv.1612.01485,
title = {Asymptotically optimal control for a simplest distributed system},
author = {Alexander Ovseevich and Aleksey Fedorov},
journal= {arXiv preprint arXiv:1612.01485},
year = {2017}
}
Comments
5 pages; the subject has grown out of studies arXiv:1308.6090 and arXiv:1611.09669; published version