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Advances in the Theory of Control, Signals and Systems with Physical Modeling pp 49–64Cite as

Iterative Learning Control Using Stochastic Approximation Theory with Application to a Mechatronic System

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 407))

Abstract

In this paper it is shown how Stochastic Approximation theory can be used to derive and analyse well-known Iterative Learning Control algorithms for linear systems. The Stochastic Approximation theory gives conditions that, when satisfied, ensure almost sure convergence of the algorithms to the optimal input in the presence of stochastic disturbances. The practical issues of monotonic convergence and robustness to model uncertainty are considered. Specific choices of the learning matrix are studied, as well as a model-free choice. Moreover, the model-free method is applied to a linear motor system, leading to greatly improved tracking.

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Author information

Authors and Affiliations

  1. Automatic Control Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland

    Mark Butcher & Alireza Karimi

Authors
  1. Mark Butcher
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  2. Alireza Karimi
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Editor information

Editors and Affiliations

  1. CAS, Unité Mathématiques et Systémes, MINES-ParisTech, 35, rue Saint-Honoré, 77300, Fontainebleau, France

    Jean Lévine

  2. Laboratoire d’ Automatique, Faculté des Sciences de l’Ingénieur Station 9, CH-1015, Lausanne, Switzerland

    Philippe Müllhaupt

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Butcher, M., Karimi, A. (2010). Iterative Learning Control Using Stochastic Approximation Theory with Application to a Mechatronic System. In: Lévine, J., Müllhaupt, P. (eds) Advances in the Theory of Control, Signals and Systems with Physical Modeling. Lecture Notes in Control and Information Sciences, vol 407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16135-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-16135-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16134-6

  • Online ISBN: 978-3-642-16135-3

  • eBook Packages: EngineeringEngineering (R0)

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