An H1 approach to iterative learning control design for uncertain systems

This note deals with the problem of designing an iterative learning control for uncertain systems. Given a linear time-invariant plant with multiplicative perturbations, a suucient condition for the convergence of the learning process for all the plant uncertainty is derived. Based on the obtained suucient condition, we show that the iterative learning control design can be reformulated as the general H 1 problem setup and thus the iterative learning controller can be designed by the well-known H 1 control design procedures. 1 1. Introduction Since the idea of iterative learning control was introduced for accurate tracking of robot trajectories by Arimoto et al. (1984), a great deal of attention has been paid to this area and plenty of results have been obtained by many researchers. Like the initial iterative learning control by Arimoto et al., most iterative learning control schemes considered in the literature are purely feedforward actions depending wholly on the previous control performance of identical tasks and hence the resulting control systems are basically open-loop. Thus, the iterative learning control cannot be used to stabilize unstable systems nor to improve the tracking performance for general trajectories. Furthermore, it is unlikely to remain robust against nonrepeatable disturbances and parameter variation, which precludes the adoption of the iterative learning control in real applications despite its advantageous features. As a means to overcome these drawbacks and to make the iterative learning control more practical, a feedback control to enhance the system robustness is commonly employed along with the iterative learning control In such control schemes, the feedback controller ensures the closed-loop stability and suppresses exogenous disturbances and the iterative learning controller provides a better tracking performance over a speciic trajectory utilizing the past information. In most of the previous work, however, the learning control design does not take the plant uncertainty into consideration explicitly, though the iterative learning controller is adopted to obtain ner tracking accuracy under plant uncertainty. Consequently, design methodology guaranteeing the convergence of the iterative learning process in the presence of the plant uncertainty is not satisfactorily discussed. Taking account of these issues, we propose an iterative learning control scheme for uncertain feedback systems and present a suucient condition for the convergence of the iterative learning process despite the plant uncertainty. The learning is conducted in a feedback connguration and the input update law of the iterative learning control is given in the frequency domain. The