Comments on 'On the equivalence of causal LTI iterative learning control and feedback control'

The area of iterative learning control (ILC) now has a large and increasing body of research with an increasing number of applications (supported by a sizable number of actual experimental veri.cation studies). The paper (Goldsmith, 2002) contains a number of assumptions and technical errors that invalidate its conclusion that normal feedback control is preferable to causal ILC, and the purpose of this note is to state the problems with this paper and clearly articulate the technical and practical validity of the ILC concept. Of course, causal ILC (in the sense of Goldsmith (2002)) is not the only option for the community and, implicitly, non-causal control structures may improve performance and other desirable closed-loop properties. Indeed, see, for example, Amann, Owens, and Rogers (1998), there is already much published work which (as one possible choice) uses optimal control concepts to produce convergent ILC algorithms that use current trial feedback plus previous trial (non-causal in the classical sense) feedforward actions. The central issue that we wish to challenge is that the proposed equivalence between causal ILC and feedback control invalidates the former and in what follows we give the details for the 4 main areas we challenge.