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

Verwoerd, Mark
and
Meinsma, Gjerrit
and
Vries, Theo de
(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 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 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 exception 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 |

Copyright: | © 2006 Elsevier |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/57734 |

Official URL: | https://doi.org/10.1016/j.automatica.2006.06.022 |

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