Updating procedures for iterative learning control in Hilbert space

The research results presented are extensions of Avrachenkov´s previous work (1998) on iterative learning control using projection-based update techniques. These updates were mainly developed for quasi-Newton optimization and also for solving systems of simultaneous equations. 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, preliminary extensions of these updating techniques to continuous systems through formulation in Hilbert space are 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