Output regulation for 1-D reaction-diffusion equation with a class of time-varying disturbances from exosystem

Abstract

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.