Observers and Disturbance Rejection Control for a Heat Equation

The article is concerned with active disturbance rejection control of a heat equation. The considered heat equation satisfies the Dirichlet boundary condition on one part of the boundary. On the other part of the boundary is located a Neumann boundary control. The heat equation system suffers from both a model uncertainty in the heat flow modeling and an unknown external disturbance. Our control approach is based on the design of an exponentially converging observer to estimates both the state and the unknown uncertainty. The estimated state and the estimated uncertainty are used to build a stabilizing feedback control law such that the closed-loop system is exponentially stabilized, and the external disturbance is rejected.