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Factorizations that relax the positive real condition in continuous-time and fast-sampled ELS schemes
Department of Electrical Engineering, Linköping University, Linkoping, Sweden. (Automatic Control)ORCID iD: 0000-0002-1927-1690
1990 (English)In: International journal of adaptive control and signal processing (Print), ISSN 0890-6327, E-ISSN 1099-1115, Vol. 4, no 5, 389-414 p.Article in journal (Refereed) Published
Abstract [en]

This paper proposes extended least-squares (ELS) for ARMAX model identification of continuous-time and certain discrete-time systems. The schemes have a relaxed strictly positive real (SPR) condition for global convergence. The relaxed SPR scheme is achieved by introducing overparametrization and prefiltering but without introducing ill-conditioning. The schemes presented are the first such proposed for continuous-time systems. The concepts developed in continuous time carry through to fast-sampled continuous-time systems and associated discrete-time ELS algorithms. For such situations, in comparison with previously proposed discrete-time schemes, the degree of overparametrization required in the proposed scheme of this paper is significantly lower. The reduction is achieved by using more suitable prefiltering and overparametrization techniques than previously proposed. We also establish the persistence of excitation (PE) of the regression vectors in the proposed ELS schemes to assure strong consistency, obtain convergence rates and provide robustness to unmodelled dynamics. To prove the PE of continuous-time regression vectors, we develop output reachability characterization for MIMO linear continuous-time systems.

Place, publisher, year, edition, pages
1990. Vol. 4, no 5, 389-414 p.
Keyword [en]
Computer Programming--Algorithms, Mathematical Techniques, ARMAX Model, Continuous-Time Systems, ELS Algorithms, Extended Least-Squares (ELS), Global Convergence, Overparametrization, Control Systems, Discrete Time
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-55445DOI: 10.1002/acs.4480040506OAI: diva2:471577
QC 20120104 NR 20140805Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2013-09-05Bibliographically approved

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Wahlberg, Bo
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