Adaptive Error Feedback Regulator Design for One-Dimensional Heat Equation With Unknown Harmonic Disturbance Anticollocated With Control

This paper considers the adaptive error feedback regulation problem for a one-dimensional heat equation with general harmonic disturbance anticollocated with control. We first construct an auxiliary system in which the control and the anticollocated disturbance become collocated and the measured error becomes the output. Then, we design an error feedback adaptive servomechanism for this system, which includes estimators for the parameters characterizing the disturbance and the reference signals. The control is thus designed to regulate the tracking error to zero and keep the states bounded.