In this paper, we consider boundary output regulation for one-dimensional reaction–diffusion equation that has disturbances entering the system from in-domain and both boundaries. The reference signal and disturbances are generated from an exosystem with time varying coefficients. First, a feedforward control is designed on the basis of an infinite-dimensional regulator equation and a backstepping transformation. Second, with the measurement output, we design an observer to estimate both states of the plant and the external system. The output feedback boundary control is then designed by replacing the states with their estimates. As a result, we show that the output converges to the reference signal exponentially as time goes on. 

　　Publication: 

　　Automatica, Volume 141, July 2022, 110274 

　　Author: 

　　Jing Wei 

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

　　Baozhu Guo 

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

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

　　Email: bzguo@iss.ac.cn