The stability for a one-dimensional unstable heat equation with nonlinear boundary uncertainty disturbance

In this note, we are concerned with the boundary stabilization of a one-dimensional heat equation with the external disturbance flowing to the control end. The nonlinear uncertainty is estimated in terms of the output, and then canceled by its estimates. We show that this strategy is valid when the derivative of the disturbance is also bounded. The numerical simulation validates the effectiveness of this method.