# American Institute of Mathematical Sciences

September  2019, 9(3): 411-424. doi: 10.3934/mcrf.2019019

## Optimal control problem for exact synchronization of parabolic system

 1 School of Mathematics and Statistics, Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, 430072, China 2 School of Science, Hebei University of Technology, Tianjin, 300400, China

* Corresponding author: Qishu Yan

Received  December 2016 Revised  September 2017 Published  April 2019

Fund Project: The first author is supported by National Natural Science Foundation of China under grants 11371285 and 11771344. The second author is supported by National Natural Science Foundation of China under grant 11701138.

In this paper, we consider the exact synchronization of a kind of parabolic system and obtain Pontryagin's maximum principle for a related optimal control problem. The method relies on the properties of the null controllability for parabolic system and an observability estimate for a linear parabolic system.

Citation: Lijuan Wang, Qishu Yan. Optimal control problem for exact synchronization of parabolic system. Mathematical Control & Related Fields, 2019, 9 (3) : 411-424. doi: 10.3934/mcrf.2019019
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