International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2569

Full Length Research Paper

Adaptive control of the generalized Korteweg-de Vries-Burgers equation

Xiaoyan Deng*, Lixin Tian and Wenxia Chen    
Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China.    
Email: [email protected]

  •  Accepted: 21 February 2012
  •  Published: 02 March 2012

Abstract

In this paper, the adaptive and non-adaptive stabilization of the generalized Korteweg-de Vries (KdV)-Burgers equation by nonlinear boundary control are analyzed. This is motivated by the method proposed by Smaoui (2004). We use this method to resolve the adaptive control of the generalized KdV-Burgers equation. For the non-adaptive case, using Lyapunov method, we show that the controlled system is exponentially stable in . As for the adaptive case, we show the  regulation of the solution of the generalized KdV-Burgers equation.

 

Key words: Adaptive control, KdV-Burgers equation, stabilization.

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