Adaptive control of Burgers' equation with unknown viscosity

In this paper, we propose a fortified boundary control law and an adaptatio n law for Burgers' equation with unknown viscosity, where no a priori knowl edge of a lower bound on viscosity is needed. This control law is decentral ized, 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-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 cannot be u sed in the present situation. Copyright (C) 2001 John Wiley & Sons, Ltd.