Stabilization of an inhomogeneous heat equation subject to constraint

In this paper, the constrained problem is investigated for an inhomogeneous heat equation with distributed load. The control objectives are to develop the control law so that the temperature can track a desired reference signal, and ensure that the temperature remains in a constrained space. We show that, with the proposed sliding-mode control method, the tracking error is bounded stable without violation of the constraint. Extensive simulations are provided to illustrate the performance of the control system.