Frequency-Domain Analysis of Robust Monotonic Convergence of Norm-Optimal Iterative Learning Control

Abstract

In this paper, we consider the norm-optimal iterative learning control (NO-ILC) framework and study its robust monotonic convergence (RMC) against model uncertainties in single-input-single-output linear time-invariant systems. Modeling errors in general degrade the convergence performance of NO-ILC, and hence ensuring RMC against model uncertainties is important. Although the robustness of NO-ILC has been studied in the literature, determining the allowable range of modeling errors for a given NO-ILC design is still an open research question. To fill this gap, a frequency-domain analysis with a multiplicity formulation of model uncertainty is developed in this paper to quantify and visualize the allowable modeling errors. Compared with the traditional formulation, the proposed new uncertainty formulation provides a less conservative representation of the allowable model uncertainty range by taking additional phase information into account and thus allows for a more complete evaluation of the robustness of NO-ILC. The analysis also clarifies how the RMC region changes as a function of NO-ILC weighting parameters and therefore can be used as a frequency-domain design tool to achieve RMC for given model uncertainties. Simulation examples are given to confirm the theoretical conclusions and demonstrate the utility of the developed analysis.