引用本文: 周华成.自抗扰控制对边界带有干扰的非线性sine-Gordon方程的镇定[J].控制理论与应用,2022,39(9):1633~1640.[点击复制] ZHOU Hua-cheng.Stabilization of a nonlinear sine-Gordon equation with boundary input disturbances via active disturbance rejection control[J].Control Theory and Technology,2022,39(9):1633~1640.[点击复制]

Stabilization of a nonlinear sine-Gordon equation with boundary input disturbances via active disturbance rejection control

DOI编号  10.7641/CTA.2021.10104
2022,39(9):1633-1640

 作者 单位 E-mail 周华成* 中南大学 数学与统计学院 hczhou@amss.ac.cn

本文讨论边界具有内部不确定和外部扰动的非线性sine-Gordon方程的镇定问题. 为处理sine-Gordon方程中的非线性项, 文章给出一个新的总扰动观测器在线估计未知扰动, 并通过自抗扰控制方法, 设计一个控制器使得在反馈控制中实时补偿(消除)总扰动. 闭环系统被证明适定的并且受控系统是指数稳定而扰动观测器是有界的. 数值模拟说明提出方法的有效性.

In this paper, we consider boundary stabilization problem of an one-dimensional nonlinear sine-Gordonequation 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.