A new concept of strong controllability via the Schur complement in adaptive tracking

Bernard Bercu (1, 2, 3) , Victor Vazquez (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 ALEA - Advanced Learning Evolutionary Algorithms

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.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

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