A new concept of strong controllability via the Schur complement in 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 : We propose a new concept of strong controllability associated with the Schur complement of a suitable limiting matrix. This concept allows us to extend the previous results associated with multidimensional ARX models. On the one hand, we carry out a sharp analysis of the almost sure convergence for both least squares and weighted least squares algorithms. On the other hand, we also provide a central limit theorem and a law of iterated logarithm for these two stochastic algorithms. Our asymptotic results are illustrated by numerical simulations.
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Contributor : Bernard Bercu <>
Submitted on : Monday, November 8, 2010 - 10:34:23 AM
Last modification on : Thursday, January 11, 2018 - 6:22:36 AM

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  • HAL Id : hal-00386247, version 1
  • ARXIV : 0801.2991

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Bernard Bercu, Victor Vazquez. A new concept of strong controllability via the Schur complement in adaptive tracking. Automatica, Elsevier, 2010, 46, pp.1799-1805. ⟨hal-00386247⟩

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