Stability of Burgers-Korteweg-de Vries Equation

Author

Gao, Wenhua ; Deng, Feiqi

Author_Institution

South China Univ. of Technol., Guangzhou

fYear

2007

fDate

May 30 2007-June 1 2007

Firstpage

1922

Lastpage

1925

Abstract

For Burgers-Korteweg-de Vries(KdVB) equation defined on a finite spatial interval with unknown viscosity, a nonlinear boundary control law and an adaptation law are proposed. Based on Lyapunov direct method, the global asymptotic stability of the closed-loop system is proved. The stochastic case of Burgers-Korteweg-de Vries equation is also considered. The exponential stability of the delayed KdVB equation is also proved if the delay parameter is sufficiently small.

Keywords

Korteweg-de Vries equation; Lyapunov methods; adaptive control; asymptotic stability; boundary-value problems; closed loop systems; delays; nonlinear control systems; stochastic systems; Lyapunov direct method; adaptation law; adaptive control; closed-loop system; delayed stochastic Burgers-Korteweg-de Vries equation stability; exponential stability; finite spatial interval; global asymptotic stability; nonlinear boundary control law; Adaptive control; Asymptotic stability; Automatic control; Automation; Boundary conditions; Delay effects; Educational institutions; Lyapunov method; Nonlinear equations; Viscosity; adaptive control; boundary control; stability;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Automation, 2007. ICCA 2007. IEEE International Conference on

Conference_Location

Guangzhou

Print_ISBN

978-1-4244-0818-4

Electronic_ISBN

978-1-4244-0818-4

Type

conf

DOI

10.1109/ICCA.2007.4376696

Filename

4376696