Adaptive Error Feedback Output Regulation for Parabolic PDEs with Unknown Disturbance

In this paper, we are concerned with the error feedback regulator problem for one-dimensional reaction-diffusion equation with general harmonic disturbance anti-collocated with control, while the tracking error collocated with the control. We construct a target system in order to make the control and anti-collocated disturbance become collocated, and make the measured error become the output. Then the error feedback adaptive servomechanism for the system is given in which the parameters of the disturbance and the reference signals are estimated. The backstepping approach is adopted in the investigation. It is shown that the proposed adaptive control law regulate the tracking error to zero and keep the state bounded.