On equivalence classes in iterative learning control

This paper advocates a new approach to study the relation between causal iterative learning control (ILC) and conventional feedback control. Central to this approach is the introduction of the set of admissible pairs (of operators) defined with respect to a family of iterations. Considered are two problem settings: standard ILC, which does not include a current cycle feedback (CCF) term and CCF-ILC, which does. By defining an equivalence relation on the set of admissible pairs, it is shown that in the standard ILC problem there exists a bijective map between the induced equivalence classes and the set of all stabilizing controllers. This yields the well-known Youla parameterization as a corollary. These results do not extend in full generality to the case of CCF-ILC; though gain every admissible pair defines a stabilizing equivalent controller, the converse is no longer true in general.