Fixed point theorem based iterative learning control for LTV systems with input singularity

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 sequence can either enter and remains ultimately in a designated neighborhood of the target trajectory, or bounded by a class 𝒦; function. Finally an illustrative examples is presented.