Time optimal sampled-data controls for heat equations
Abstract
In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls. Our design is reasonable from perspective of sampled-data controls. And it might provide a right way for the numerical approach of a time optimal distributed control problem, via the corresponding semi-discretized (in time variable) time optimal control problem. The study of such a time optimal sampled-data control problem is not easy, because it may have infinitely many optimal controls. We find connections among this problem, a minimal norm sampled-data control problem and a minimization problem. And obtain some properties on these problems. Based on these, we not only build up error estimates for optimal time and optimal controls between the time optimal sampled-data control problem and the time optimal distributed control problem, in terms of the sampling period, but also prove that such estimates are optimal in some sense.
Keywords
Cite
@article{arxiv.1701.06116,
title = {Time optimal sampled-data controls for heat equations},
author = {Gengsheng Wang and Donghui Yang and Yubiao Zhang},
journal= {arXiv preprint arXiv:1701.06116},
year = {2017}
}