This paper studies the adaptive control problem of the Korteweg-de Vries-Burgers equation. Using the Lyapunov function method, we prove that the closed-loop system including the parameter estimator as a dynamic component is globally stable. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's lemma which cannot be used in the present situation. The closed-loop system is shown to be well posed.
Xiaoyan Deng. Lixin Tian. Wenxia Chen. "Adaptive Stabilization of the Korteweg-de Vries-Burgers Equation with Unknown Dispersion." J. Appl. Math. 2012 1 - 12, 2012. https://doi.org/10.1155/2012/389450