Stochastic Iterative Learning Control for Lumped- and Distributed-Parameter Systems: A Wiener-Filtering Approach
Andreas Deutschmann, G. Stadler, Andreas Kugi
Abstract
This article presents a stochastically optimal iterative learning control (ILC) approach by designing a general integral learning operator which minimizes the expected mean-squares output error. The proposed learning law generalizes existing optimal PD-type learning laws and the resulting optimal learning operator turns out to be the solution of the noncausal Wiener-Hopf equation. The proposed solution can be interpreted as a systematic dual to traditional norm-optimal ILC schemes with superior asymptotic properties under stochastic perturbations. While the fully optimal solution is inherently iteration-varying, a simpler suboptimal learning operator with less computational effort is introduced. Moreover, a numerically very efficient strategy based on the fast Fourier transform is presented to obtain numerical solutions of the learning operator. By avoiding the need of spectral factorizations or solutions to Riccati equations, this approach is directly applicable to a certain class of distributed-parameter systems. Finally, the Wiener-filter-based ILC algorithm is demonstrated on finite- and infinite-dimensional example problems.