Recursive identification of switched ARX hybrid models: Exponential convergence and persistence of excitation

René Vidal*, Brian D.O. Anderson

*Corresponding author for this work

    Research output: Contribution to journalConference articlepeer-review

    20 Citations (Scopus)

    Abstract

    We propose a recursive identification algorithm for a class of discrete-time linear hybrid systems known as Switched ARX models. The key to our approach is to view the identification of multiple ARX models as the identification of a single, though more complex, lifted dynamical model in a higher dimensional space. Since the dynamics of this lifted model do not depend on the value of the discrete state or the switching mechanism, we propose to use a standard recursive identifier in the lifted space. We derive persistence of excitation conditions on the input/output data guarantee the exponential convergence of the recursive identifier. Such conditions are a natural generalization of the well known result for ARX models. We then use the estimates of the lifted model parameters to build a homogenous polynomial whose derivatives at a regressor give an estimate of the parameters of the ARX model generating that regressor. Although our algorithm is designed for the case of perfect input/output data, our experiments also show its performance with noisy data.

    Original languageEnglish
    Article numberTuA01.6
    Pages (from-to)32-37
    Number of pages6
    JournalProceedings of the IEEE Conference on Decision and Control
    Volume1
    DOIs
    Publication statusPublished - 2004
    Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
    Duration: 14 Dec 200417 Dec 2004

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