Iterative Learning Control for Singularly Perturbed Systems

The singularly perturbed systems are described by diierential equations with a small parameter near higher derivatives. It turns out that most of known iterative learning control algorithms diverge in the presence of singular perturbations. The aim of the present paper is to construct learning control algorithms that are able to overcome this problem. Our approach is based on weak convergence conditions that take into account the whole range of frequency response characteristic in contrast to traditional convergence conditions based on the rough H 1 norm. The rst two proposed methods employ the analog and digital ltering. Whereas the learning operator of the third method approximates the inverse of the regular part of the system and at the same time appears to be a low-pass lter. The simulation of the algorithms for a benchmark model connrms all theoretical considerations.