Convergence analysis of iterative learning control with uncertain initial conditions

This paper explores convergence problem of iterative learning control (ILC) for linear discrete-time multivariable systems with uncertain initial conditions from two-dimensional (2-D) notion. The iterative learning process is described by a 2-D learning model, which includes both the system dynamics and the learning process. A simple ILC rule is used and the effect of tracking errors against varying initial conditions is investigated. Based on 2-D system theory, the conditions of the convergence of the learning control rules are proposed. It is shown that the learning rule can be guaranteed to converge with respect to small perturbations of the system parameters even though the initial condition of each iteration is variable.