Mathematical methods

Abstract

The chapter provides the mathematical background needed for the development of a general theory and generally applicable algorithms for Iterative Learning Control. Ranging from matrix methods to system representation using linear operators mapping input Hilbert spaces into output Hilbert spaces, the fundamental relationships defining the solutions of minimum norm and linear quadratic problems are found using adjoint operators. This is followed by an analysis of the ideas of convergence which are defined precisely using spectral concepts, convexity and the notion of successive (alternating) projection.