控制非线性水波:Korteweg-de Vries-Burgers方程的边界稳定

Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251) Pub Date : 1999-06-02 DOI:10.1109/ACC.1999.786108

Weijiu Liu, M. Krstić

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引用次数: 4

摘要

研究了Korteweg-de Vries-Burgers方程在定域[0,1]上的边界反馈全局指数镇定问题。我们导出了u(0)=u/下标x/(1)=u/下标xx/(1)-k[u(1)/sup 3/+ u(1)]=0的控制律，其中k是一个足够大的正常数，并证明了它保证了L/sup 2/-全局指数稳定性、H/sup 1/-全局渐近稳定性和H/sup 1/半全局指数稳定性。闭环系统具有良好的定姿性。

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Controlling nonlinear water waves: boundary stabilization of the Korteweg-de Vries-Burgers equation

The problem of global exponential stabilization by boundary feedback for the Korteweg-de Vries-Burgers equation on the domain [0,1] is considered. We derive a control law of the form u(0)=u/sub x/(1)=u/sub xx/(1)-k[u(1)/sup 3/+ u(1)]=0, where k is a sufficiently large positive constant, and prove that it guarantees L/sup 2/-global exponential stability, H/sup 1/-global asymptotic stability, and H/sup 1/ semi-global exponential stability. The closed-loop system is shown to be well posed.

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Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)

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