Backstepping boundary control for semilinear parabolic PDEs

This paper presents an infinite-dimensional back-stepping for boundary stabilization of semilinear parabolic PDEs. The feedback control law is developed from the feedback control law obtained for the linear parabolic PDEs. The actuation is only at one end of the domain. We proved local H⁴ exponential stability of the closed-loop system based on construction of a strict Lyapunov function. The design is tested to boundary stabilization of the Fisher´s equation.