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.
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Contributor : Bernard Bercu <>
Submitted on : Wednesday, May 20, 2009 - 5:11:37 PM
Last modification on : Thursday, January 11, 2018 - 6:22:36 AM

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



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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