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

Verwoerd, Mark and Meinsma, Gjerrit and de Vries, Theo (2006) On admissible pairs and equivalent feedback - Youla parameterization in iterative learning control. Automatica, 42 (12). pp. 2079-2089. ISSN 0005-1098

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Abstract

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 casual 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 rebustly 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 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 concides with the Youla parameterization of all stabilizing controllers (stable plant case). The second part of the paper considers the general family of CCF-iterations. Results derived in the non-CCF case carry over, with the execption that the set of equivalent controllers now forms but a subset of all stabilizing controllers. Necessary and sufficient conditions for full generalization are given.

Item Type: Article
Additional Information: The original publication is available at http://www.elsevier.com/wps/find/journaldescription.cws_home/270/description#description
Keywords: Iterative learning control; Youla parameterization; Feedback control; Hx control; Equivalent control; Linear systems; Hamilton Institute.
Subjects: Science & Engineering > Hamilton Institute
Item ID: 941
Identification Number: 10.1016/j.automatica.2006.06.022
Depositing User: Mark Verwoerd
Date Deposited: 15 Apr 2008
Journal or Publication Title: Automatica
Publisher: Elsevier
Refereed: Yes
URI:

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