Optimal Iteration-Varying Iterative Learning Control for Systems with Stochastic Disturbances

This paper examines the problem of Iterative Learning Control (ILC) design for systems with stochastic disturbances and noise. Stochastic inputs are particularly problematic in ILC because they can be propagated many iterations forward by the iterative algorithm, severely limiting performance. The approach developed here is based on minimizing the error power spectrum from iteration-to-iteration, so as to achieve fastest convergence. The optimization is performed in the frequency domain resulting in an iteration-varying solution for the optimal ILC filters. It is shown that the filters are dependent on a ratio of power spectrums of deterministic inputs to stochastic inputs, which affects convergence rate. Convergence is slowest for frequencies where the deterministic-to-stochastic ratio is small. A numerical example is presented comparing the iteration-varying solution developed here to a popular heuristic algorithm