UDE-based robust boundary control for an unstable parabolic PDE with unknown input disturbance

A novel control strategy, named uncertainty and disturbance estimator (UDE)-based robust control, is applied to the stabilization of an unstable parabolic partial differential equation (PDE) with a Dirichlet type boundary actuator and an unknown time-varying input disturbance. The unstable PDE is stabilized by the backstepping approach, and the unknown input disturbance is compensated by the UDE, which constructs an estimation of the disturbance by filtering the system input and measurable state signals. The proposed UDE-based robust boundary control only requires the spectrum information of the disturbance signal and one boundary output measurement. Stability analysis of the closed-loop systems is carried out, and a numerical example is provided to validate the proposed method.