Constrained Adaptive Control for Heat Equations with Disturbances

This paper considers the adaptive stabilization for uncertain heat equations via constrained boundary control and constrained distributed control, respectively. Quite essentially, distributed disturbance and boundary disturbance are simultaneously allowed in the considered heat equations, and moreover, only a boundary value is available for feedback in the case of boundary control. This renders the equations under investigation more practical and the control problem more challenging. In this paper, a new adaptive control scheme is proposed to effectively deal with disturbances and to properly satisfy the pre-specified control constraints. Specifically, adaptive dynamic compensation technique and appropriate projection operator are first introduced respectively to handle the disturbances and the control constraints. Then, the constrained boundary and distributed controllers are successfully constructed, which guarantee that all states of the resulting closed-loop systems are bounded in certain sense of norms.