自抗扰控制对边界带有干扰的非线性sine-Gordon方程的镇定

In this paper, we consider boundary stabilization problem of an one-dimensional nonlinear sine-Gordon equation with boundary control matched unknown nonlinear internal uncertainty and external disturbance. To cope with the nonlinear term of sine-Gordon equation, we propose a new total disturbance estimator to recover the disturbance. By the active disturbance rejection control strategy, we design a stabilizing feedback control law by compensating (cancelling) the total disturbance. It is shown that the resulting closed-loop system is well-posed and the controlled part of system is exponentially stable while the disturbance estimator is bounded. The numerical experiments are carried out to show the effectiveness of the proposed method.