Backstepping boundary control of Burgers' equation with actuator dynamics

In this paper, we propose a backstepping boundary control law for Burgers' equation with actuator dynamics. While the control law without actuator dyn amics depends only on the signals u(0,t) and u(1,t), the backstepping contr ol also depends on u(x)(0, t), u(x)(1, t), u(xx)(0, t) and u(xx)(1,t), maki ng the regularity of the control inputs the key technical issue of the pape r. With elaborate Lyapunov analysis, we prove that all these signals are su fficiently regular and the closed-loop system, including the boundary dynam ics, is globally H-3 Stable and well posed. (C) 2000 Elsevier Science B.V. All rights reserved.