Adaptive regulator design of a viscous Burgers' system by boundary control

This paper is concerned with adaptive stabilization and regulator design for a viscous Burgers' equation by nonlinear boundary control. Under the existence of bounded deterministic disturbances, the adaptive regulator is constructed by the concept of high‐gain nonlinear output feedback and the estimation mechanism of the unknown parameters. In the control system the global asymptotic stability and the convergence of the system state to zero will be guaranteed. It is shown that the theory can be generalized to the systems with higher‐order nonlinearity.