Iterative Machine Learning for Output Tracking

This paper develops a frequency-domain iterative machine learning (IML) approach for output tracking. Frequency-domain iterative learning control allows bounded noncausal inversion of system dynamics and is, therefore, applicable to nonminimum phase systems. The model used in the frequency-domain control update can be obtained from the input-output data acquired during the iteration process. However, such data-based approaches can have challenges if the noise-to-output-signal ratio is large. The main contribution of this paper is the use of kernel-based machine learning during the iterations to estimate both the model (and its inverse) for the control update, as well as the model uncertainty needed to establish bounds on the iteration gain for ensuring convergence. Another contribution is the proposed use of augmented inputs with persistency of excitation to promote learning of the model during iterations. The improved model can be used to better infer the inverse input resulting in lower initial error for new output trajectories. The proposed IML approach with the augmented input is illustrated with simulations for a benchmark nonminimum phase example.