Sliding mode and active disturbance rejection control to stabilization of one-dimensional anti-stable wave equations subject to disturbance in boundary input

We propose two strategies to stabilize a one-dimensional anti-stable wave equation subject to boundary disturbance, namely, sliding mode control (SMC) and the active disturbance rejection control (ADRC). The finite “reaching condition”, and the existence and uniqueness of the solution for all states in the state space in SMC are established. We also develop an ADRC to attenuate the disturbance and show that this strategy works well when the derivative of the disturbance is also bounded. Simulation examples are presented for both control strategies.