Updating Procedures for Iterative Learning Control in Hilbert Space

The research results presented here are extensions of previous work on Iterative Learning Control (ILC) using projection-based update techniques. These updates were mainly developed for Quasi-Newton optimization and also for solving systems of simultaneous equations. Recently, such updates have been used by the authors to estimate the dynamics of a control system which is asked to perform a periodic task using a discrete formulation. In addition, recently, preliminary extensions of these updating techniques to continuous systems through formulation in ZHilbert Space have been proposed. This paper provides a formulation of the Iterative Learning Control problem in Hilbert Space with a convergence proof of the proposed solution based on Broyden's update.