Brief paper: A new concept of strong controllability via the Schur complement for ARX models in adaptive tracking

Authors:
Bernard Bercu;Victor Vazquez
Affiliations:
Université Bordeaux 1, Institut de Mathématiques de Bordeaux, UMR CNRS 5251, and INRIA Bordeaux, team CQFD, 351 cours de la libération, 33405 Talence cedex, France;Universidad Autónoma de Puebla, Facultad de Ciencias Fisico Matemáticas, Avenida San Claudio y Rio Verde, 72570 Puebla, Mexico
Venue:
Automatica (Journal of IFAC)
Year:
2010

Citing 10
Cited 0

Further Results on Least Squares Based Adaptive Minimum Variance Control

SIAM Journal on Control and Optimization
Convergence and logarithm laws of self-tuning regulators

Automatica (Journal of IFAC)
Weighted Estimation and Tracking for ARMAX Models

SIAM Journal on Control and Optimization
Central Limit Theorem And Law Of Iterated Logarithm For Least Squares Algorithms In Adaptive Tracking

SIAM Journal on Control and Optimization
Random Iterative Models

Random Iterative Models
A Method to Search ARX Model Orders and Its Application to Sales Dynamics Analysis

ICDMW '06 Proceedings of the Sixth IEEE International Conference on Data Mining - Workshops
Decentralized tracking-type games for multi-agent systems with coupled ARX models: Asymptotic Nash equilibria

Automatica (Journal of IFAC)
Recursive identification of switched ARX systems

Automatica (Journal of IFAC)
Kernel Density Estimation and Goodness-of-Fit Test in Adaptive Tracking

SIAM Journal on Control and Optimization
A hybrid model for stock market forecasting and portfolio selection based on ARX, grey system and RS theories

Expert Systems with Applications: An International Journal

Quantified Score

Hi-index	22.14

Visualization

Abstract

We propose a new concept of strong controllability related to the Schur complement of a suitable limiting matrix. This new notion allows us to extend the previous convergence results associated with multidimensional ARX models in stochastic adaptive tracking. 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 algorithms.