Estimation of viscosity and controller strengthening in boundary stabilization of Burgers´ equation

We propose a fortified boundary control law and an adaptation law for Burgers´ equation with unknown viscosity, where no a priori knowledge of a lower bound on viscosity is needed. This control law is decentralized, i.e., implementable without the need for central computer and wiring. Using the Lyapunov method, we prove that the closed-loop system, including the parameter estimator as a dynamic component, is globally H/sup 1/ stable and well posed. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat´s Lemma which can not be used in the present situation.