Boundary output feedback stabilisation for a wave equation with a quadratic-cubic nonlinear boundary condition and disturbance

This paper investigates the boundary output feedback exponential stabilisation for a wave equation with a quadratic-cubic nonlinear boundary condition and unknown control-matched disturbance. Utilising the boundary measurement outputs, an infinite-dimensional disturbance estimator is designed to estimate the boundary disturbance, with the resulting estimation error possessing integral exponential convergence. Subsequently, via the active disturbance rejection control strategy, a boundary output feedback stabilising controller is designed based on the disturbance estimate that effectively compensates the boundary disturbance. The resulting closed-loop system is proven to be exponentially stable. Finally, numerical simulations are performed to confirm the effectiveness of the proposed approach.