Performance boundary output tracking for one-dimensional heat equation with boundary unmatched disturbance

In this paper, we consider boundary output tracking for a one-dimensional heat equation with external disturbance at the opposite end of the bar. First, an unknown input infinite-dimensional observer is designed and an estimate of disturbance is obtained from the observer. Second, with reference signal and estimate of disturbance, we design a servo system which has bounded solution given that the reference signal and its derivative are bounded. The output feedback boundary control is then designed by the states of servo system and observer. It is proved that the state of closed-loop system tracks the state of the servo system. As a result, the output tracking is included. Finally, some simulation results are presented to illustrate the effectiveness of the proposed scheme. (C) 2018 Elsevier Ltd. All rights reserved.