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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