Iterative Learning Control for a Class of Inhomogeneous Heat Equations

This paper addresses the boundary control problem of heat equations under the framework of iterative learning control (ILC). Without any simplification or discretization of the 3D dynamics in the time, space as well as iteration domains, the learning convergence of ILC is guaranteed through rigorous analysis by transforming the inhomogeneous heat equation into its integral form and exploiting the properties of the embedded Jacobi Theta functions. The proposed scheme not only makes anticipatory compensation possible to overcome the heat conduction delay in boundary output tracking, but also eliminates the gain margin limitation encountered in feedback control. In the end, an illustrative example is presented to demonstrate the performance of the proposed ILC scheme.