Monotonic convergence of iterative learning control for uncertain systems using a time-varying filter

Iterative learning control (ILC) is a learning technique used to improve the performance of systems that execute the same task multiple times. Learning transient behavior has emerged as an important topic in the design and analysis of ILC systems. In practice, the learning control is often low-pass filtered with a "Q-filter" to prevent transient growth, at the cost of performance. In this note, we consider linear time-invariant, discrete-time, single-input single-output systems, and convert frequency-domain uncertainty models to a time-domain representation for analysis. We then develop robust monotonic convergence conditions, which depend directly on the choice of the Q-filter and are independent of the nominal plant dynamics. This general result is then applied to a class of linear time-varying Q-filters that is particularly suited for precision motion control.