Output Regulation of Wave Equation with General Disturbance

Abstract

In this paper, we consider an output regulation problem for a one-dimensional wave equation subject to general boundary disturbance. The disturbance is estimated by another wave system which can be regarded as extended state observer from active disturbance rejection control. We design a servo system based on the disturbance estimator and the measurable regulation error. The output feedback control law is then established by involving the states of servo system and observer system only. As a result, we obtain the regulation error is convergent to zero exponentially as time goes to infinity. At the same time, all states of the closed-loop system are shown to be uniformly bounded. Numerical simulation is also presented to validate the theoretical results.