On the usefulness of persistent excitation in ARX adaptive tracking

Bernard Bercu 1, 2, 3 Victor Vazquez 1, 2
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
3 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : The usefulness of persistent excitation is well-known in the control community. Thanks to a persistently excited adaptive tracking control, we show that it is possible to avoid the strong controllability assumption recently proposed in the multidimensional ARX framework. We establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters. A central limit theorem and a law of iterated logarithm are also provided. All this asymptotical analysis is related to the Schur complement of a suitable limiting matrix.
Type de document :
Article dans une revue
International Journal of Control, Taylor & Francis, 2010, 83, pp.1145-1154
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https://hal.archives-ouvertes.fr/hal-00386177
Contributeur : Bernard Bercu <>
Soumis le : mercredi 20 mai 2009 - 17:11:37
Dernière modification le : mercredi 29 novembre 2017 - 15:10:37

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  • HAL Id : hal-00386177, version 1
  • ARXIV : 0903.2572

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Bernard Bercu, Victor Vazquez. On the usefulness of persistent excitation in ARX adaptive tracking. International Journal of Control, Taylor & Francis, 2010, 83, pp.1145-1154. 〈hal-00386177〉

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