  Iterative learning control (ILC) is capable of improving the tracking
performance of repetitive control systems by utilizing data from past
iterations. The aim of this paper is to achieve both task flexibility, which is
often achieved by ILC with basis functions, and the performance of
frequency-domain ILC, with an intuitive design procedure. The cost function of
norm-optimal ILC is determined that recovers frequency-domain ILC, and
consequently, the feedforward signal is parameterized in terms of basis
functions and frequency-domain ILC. The resulting method has the performance
and design procedure of frequency-domain ILC and the task flexibility of basis
functions ILC, and are complimentary to each other. Validation on a benchmark
example confirms the capabilities of the framework.
