On inversion-based approaches for feedforward and ILC

System inversion is at the basis of many feedforward and learning control algorithms. The aim of this paper is to analyze several of these approaches in view of their subsequent use, showing inappropriate use that is previously overlooked. This leads to different insights and new approaches for both feedforward and learning. The methods are compared in various aspects, including finite vs. infinite preview, exact vs. approximate, and quality of inversion in various norms which directly relates to their use. In addition, extensions to (non-square) multivariable and time-varying systems are presented. The results are validated on a nonminimum-phase benchmark system.