Fixed Point Theorem based Iterative Learning Control for LTV Systems with Input Singularity

Abstract

In this work we address a challenging and open problem: how to design a suitable iterative learning control (ILC) system in the presence of input singularity, which is incurred by the singularities of the system direct feed-through term. Considering two typical types of input singularities, we first revise the ILC operators accordingly by adding a forgetting factor and incorporating a time varying learning gain, in the sequel guarantee ILC operators to be contractible. Next, using Banach fixed-point theorem, we demonstrate that the output sequence can either enter and remains ultimately in a designated neighbourhood of the target trajectory, or bounded by a class Κ function. Finally an illustrative example is presented.