The innovation algorithms for multivariable state‐space models

Summary This paper derives the input‐output representation of the dynamical system described by a linear multivariable state‐space model and the corresponding multivariate linear regressive model (ie, multivariate equation‐error model). A projection identification algorithm, a multivariate stochasti...

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Bibliographic Details
Published in:International journal of adaptive control and signal processing Vol. 33; no. 11; pp. 1601 - 1618
Main Authors: Ding, Feng, Zhang, Xiao, Xu, Ling
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 01.11.2019
Subjects:
Algorithms
Convergence
gradient search
Identification
Innovations
Multivariate analysis
multivariate system
multi‐innovation identification
Parameter estimation
Regression analysis
ISSN:0890-6327, 1099-1115
Online Access:Get full text
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Summary:Summary This paper derives the input‐output representation of the dynamical system described by a linear multivariable state‐space model and the corresponding multivariate linear regressive model (ie, multivariate equation‐error model). A projection identification algorithm, a multivariate stochastic gradient identification algorithm, and a multi‐innovation stochastic gradient (MISG) identification algorithm are proposed for multivariate equation‐error systems by using the negative gradient search and the multi‐innovation identification theory. The convergence analysis of the MISG algorithm indicates that the parameter estimation errors converge to zero under the persistent excitation condition. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.
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ISSN:0890-6327
1099-1115
DOI:10.1002/acs.3053