Output tracking for one-dimensional heat equation subject to boundary control matched disturbance

In this paper, we are concerned with the performance output reference signal tracking for a heat equation with matched boundary disturbance. Firstly, we construct a state reference trajectory system based on the reference signal, and prove this observer system is bounded. Secondly, we design a performance output tracking controller, which can make the performance output is tracking the reference signal and cancel the external disturbance. In addition, the controller can also ensure all the internal-loops are bounded. Finally, the reference state is tracked by the state of the system, and it has been proved by Lyapunov functional method.