Bernard Bercu

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We investigate the asymptotic properties of a recursive kernel density estimator associated with the driven noise of a linear regression in adaptive tracking. We provide an almost sure pointwise and uniform strong law of large numbers as well as a pointwise and multivariate central limit theorem. We also propose a goodness-of-fit test together with some(More)
— We introduce a new concept of strong controlla-bility for ARX models in adaptive tracking. This new notion is related to the Schur complement of a suitable limiting matrix. It allows us to extend the previous convergence results associated with both least squares and weighted least squares algorithms. In particular, we show the almost sure convergence as(More)
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(More)
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