Fast iterative learning control for delay systems: A predictive approach

In a previous paper (Li et al. (2005)), an iterative learning control (ILC) law, proposed for linear continuous systems with a single time delay, has the ability to drive the output tracking error to zero only after one learning iteration. The convergence result is quite attractive; however, it requires unavailable system state. The aim of this paper is to provide a predictive approach to not only reach this result, but also extend it to linear continuous systems with multiple time delays. To this end, that unavailable system state is predicted and its corresponding equivalent form is obtained, based on which new ILC laws with fully available information are determined, ensuring the zero output tracking only after one learning iteration. The numerical simulation shows that this kind of ILC design is available, and furthermore the extension of the results from systems with a single time delay to those with multiple time delays is feasible.