On the usefulness of persistent excitation in ARX adaptive tracking

Abstract

The usefulness of persistent excitation is well known in the control community. Using a persistently excited adaptive tracking control, we show that it is possible to avoid the strong controllability assumption recently proposed by the authors for multivariate ARX models. 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. This asymptotical analysis is related to the Schur complement of a suitable limiting matrix.

Keywords:

• estimation
• adaptive control
• persistent excitation
• Schur complement
• central limit theorem
• law of iterated logarithm

Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments which helped to improve the paper substantially. This work has been supported by INRIA, by CONACYT and by the ECOS Scientific Cooperation Programme.