Boundary Control Of Heat Equation Research Articles

UDE-based Robust Boundary Control of Heat Equation with Unknown Input Disturbance

In this paper, a novel robust control strategy named uncertainty and disturbance estimator (UDE) is applied to the stabilization of an unstable heat equation with Dirichlet type boundary actuator and unknown time-varying input disturbance. The system is stabilized by the backstepping approach and the unknown input disturbance is compensated by the UDE-based method which constructs an estimation of the disturbance through filtering the system input U(t) and boundary state u(1, t). Compared to other existing disturbance compensation methods, the UDE-based method only requires the spectrum information of the disturbance signal. Furthermore, the output feedback version of the proposed control is also derived for the practical implementation purpose. Stability analysis of the closed-loop system for both state feedback and output feedback cases are carried out and simulation examples are also provided to verify the proposed method.

On the Reachable States for the Boundary Control of the Heat Equation

We are interested in the determination of the reachable states for the boundary control of the one-dimensional heat equation. We consider either one or two boundary controls. We show that reachable states associated with square integrable controls can be extended to analytic functions on some square of C, and conversely, that analytic functions defined on a certain disk can be reached by using boundary controls that are Gevrey functions of order 2. The method of proof combines the flatness approach with some new Borel interpolation theorem in some Gevrey class with a specified value of the loss in the uniform estimates of the successive derivatives of the interpolating function.