Sliding mode boundary control for exponential stabilization of linear parabolic distributed parameter systems subject to external disturbance

In this article, we are concerned with the exponential stabilization of parabolic distributed parameter systems with Neumann/mixed boundary conditions and external disturbance. To deal with the bounded disturbance, a sliding mode boundary control scheme is adopted based on the backstepping method. Firstly, the exponential stability of the considered system is proven along the selected sliding surface. Secondly, a sliding mode boundary controller is designed to regulate the closed-loop system trajectory to a suitable sliding surface within a prescribed time and then maintain the sliding motion on the surface. Thirdly, on the chosen sliding surface, the closed-loop system with the sliding mode boundary controller is exponentially stable. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results.