On admissible pairs and equivalent feedback - Youla parameterization in iterative learning control

This paper revisits a well-known synthesis problem in iterative learning control, where the objective is to optimize a performance criterion over a class of causal iterations. The approach taken here adopts an infinite-time setting and looks at limit behavior. The first part of the paper considers iterations without current-cycle-feedback (CCF) term. A notion of admissibility is introduced to distinguish between pairs of operators that define a robustly converging iteration and pairs that do not. The set of admissible pairs is partitioned into disjoint equivalence classes. Different members of an equivalence class are shown to correspond to different realizations of a (stabilizing) feedback controller. Conversely, every stabilizing controller is shown to allow for a (non-unique) factorization in terms of admissible pairs. Class representatives are introduced to remove redundancy. The smaller set of representative pairs is shown to have a trivial parameterization that coincides with th...

• Type: Journal
• Year: 2006
• Where: AUTOMATICA
• Authors: Mark Verwoerd, Gjerrit Meinsma, Theo de Vries
• Keywords: Admissible Pairs, AUTOMATICA 2006, Iteration, Well-known Synthesis Problem