Adaptive Internal Model Based Tracking and Disturbance Rejection for 1-D Reaction-Diffusion Equation

In this paper, we consider the problem of output regulation of one-dimensional reaction diffusion equation. Disturbance with unknown frequency are generated by an unknown finite dimensional exosystem into all possible channels, including internal and boundary channels of the equation. This paper intends to use the principle of adaptive internal model, and through the estimation of unknown frequency, can design a feedback control based on tracking error to realize the output regulation and disturbance rejection of the reaction-diffusion equation. The important significance of this problem is that the frequency of disturbance is unknown, and both the control and observation operators are unbounded.