Finite-Time Stabilization for a Chaos Wave Equation with Disturbance

In this article, we investigate the output feedback finite-time stabilization for a chaotic wave equation with a superlinear boundary condition. Using two boundary measurements as output signals, a disturbance estimator is designed to estimate the total disturbance in the sense that the estimation error signal is convergent to zero in finite-time. Based on the estimated total disturbance, an observer is proposed to make the observer state convergent to the state of the original system in finite-time, which essentially improves the result of [IEEE Trans. Automat. Control, 69(10), 6762-6776, 2024]. Finally, by means of the active disturbance rejection control strategy, we derive an observer-based output feedback stabilizing control law. It is shown that the resulting closed-loop system is finite-time stable while the disturbance estimator is bounded. Numerical simulations are performed to validate the effectiveness of the proposed approach.