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Factorizations that relax the positive real condition in continuous‐time and fast‐sampled ELS schemes
Author(s) -
Krishnamurthy Vikram,
Wahlberg Bo,
Moore John B.
Publication year - 1990
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480040506
Subject(s) - reachability , robustness (evolution) , control theory (sociology) , discrete time and continuous time , mathematics , convergence (economics) , mimo , computer science , algorithm , mathematical optimization , biochemistry , chemistry , statistics , control (management) , artificial intelligence , economics , gene , economic growth , beamforming
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.