Adaptive Stabilization of a Class of Reaction–Diffusion Systems

Abstract

This paper is concerned with adaptive stabilization of a class of reaction–diffusion systems governed by a nonlinear partial differential equation of the first order in time but the fourth order in space. In the presence of bounded deterministic disturbances, the adaptive stabilizer 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.