Disturbance Estimator-Based Boundary Control for a Chaotic Wave System With Disturbance

In this paper, boundary output feedback exponential stabilization and disturbance rejection for a chaotic wave system with superlinear boundary condition and unknown boundary disturbance are investigated. By using measured outputs, an infinite-dimensional disturbance estimator is designed to estimate the unknown boundary disturbance without requiring the conventional boundedness of its derivative and high gain of the estimator. A novel disturbance estimator-based boundary control, comprised of a delayed boundary output feedback control and a disturbance compensator, is then designed to guarantee exponential stability of the resulting closed-loop system. By means of characteristics method and boundary reflections, we derive two nonlinear reflection relations mainly caused by the superlinear boundary condition. The numerical simulations are performed for a chaotic system to validate the effectiveness of the proposed control approach.