D-type anticipatory iterative learning control for a class of inhomogeneous heat equations

In this paper, a D-type anticipatory iterative learning control (ILC) scheme is applied to the boundary control of a class of inhomogeneous heat equations, where the heat flux at one side is the control input while the temperature measurement at the other side is the control output. By transforming the inhomogeneous heat equation into its integral form and exploiting the properties of the embedded Jacobi Theta functions, the learning convergence of ILC is guaranteed through rigorous analysis, without any simplification or discretization of the 3D dynamics in the time, space as well as iteration domains. The adopted ILC scheme makes full use of the process repetition and deals with state-independent or state-dependent uncertainties. Meanwhile, due to the feedforward characteristic of ILC, 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.