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arXiv · 1701.06116

Time optimal sampled-data controls for heat equations

Gengsheng Wang·Donghui Yang·Yubiao Zhang
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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.

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Gengsheng Wang, Donghui Yang, Yubiao Zhang. 2017-01-22. Time optimal sampled-data controls for heat equations. https://arxiv.org/abs/1701.06116

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