Sliding Mode and Active Disturbance Rejection Control to Stabilization of One-Dimensional Anti-Stable Wave Equations Subject to Disturbance in Boundary Input

In this technical note, we are concerned with the boundary stabilization of a one-dimensional anti-stable wave equation subject to boundary disturbance. We propose two strategies, namely, sliding mode control (SMC) and the active disturbance rejection control (ADRC). The reaching condition, and the existence and uniqueness of the solution for all states in the state space in SMC are established. The continuity and monotonicity of the sliding surface are proved. Considering the SMC usually requires the large control gain and may exhibit chattering behavior, we then develop an ADRC to attenuate the disturbance. We show that this strategy works well when the derivative of the disturbance is also bounded. Simulation examples are presented for both control strategies.