The innovation algorithms for multivariable state‐space models. (17th October 2019)

• Record Type: Journal Article
• Authors: Ding, Feng; Zhang, Xiao; Xu, Ling
• Is Part Of: International journal of adaptive control and signal processing. Volume 33:Number 11(2019)
• Page Start: 1601
• Page End: 1618
• Publication Date: 2019-10-17
• Subjects: gradient search -- multi‐innovation identification -- multivariate system -- parameter estimation; Adaptive control systems -- Periodicals; Adaptive signal processing -- Periodicals; 629.836
• DOI: 10.1002/acs.3053
• Languages: English
• ISSNs: 0890-6327

Abstract

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.