Coping with actuator dynamics using backstepping for boundary stabilization of Burgers´ equation

In this paper we propose a backstepping boundary control law for Burgers´ equation with actuator dynamics. While the control law without actuator dynamics depends only on the signals u(0, t) and u(1, t), the backstepping control also depends on u/sub x/(0, t), u/sub x/(1, t), u/sub xx/(0, t) and u/sub xx/(1, t), making the regularity of the control inputs the key technical issue of the paper. With elaborate Lyapunov analysis, we prove that all these signals are sufficiently regular and the closed-loop system, including the boundary dynamics, is globally H/sup 3/ stable and well posed.