In this paper, we consider output regulation for a 1-d heat equation where the disturbances generated from an unknown finite-dimensional exosystem enter all possible channels. We adopt adaptive observer internal model approach which has been well developed for lumped parameter systems over two decades to estimate all possible unknown frequencies that have entered into a transformed system. By the estimates of the unknown frequencies, we are able to design a tracking error based feedback control to achieve output regulation and disturbance rejection for this PDE. A significance of the problem lies in the fact that both the control and observation operators are unbounded. The proposed approach is potentially applicable to other PDEs. 

　　Publication: 

　　Automatica, Volume 138, April 2022, 110159 

　　Author: 

　　Baozhu Guo 

　　School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China 

　　Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China 

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 

　　Email: bzguo@iss.ac.cn 

　　Renxi Zhao 

　　Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China 

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China