Iterative learning control: quantifying the effect of output noise

Fixed parameter iterative learning control (ILC) for linear-time invariant, single-input single-output systems subject to output noise is analysed with the intent of predicting the expectation of the underlying `noise-free` mean square error (Euclidean norm) of the time series on each iteration. Explicit formulae are obtained in terms of the `lifted` matrix models of the plant. Computational experiments are used to confirm the correctness of the proposed properties. Finally, frequency domain formulae are derived to provide insight into links between plant characteristics, noise spectra and other ILC parameters, and illustrated by application to the inverse-model-based ILC algorithm.