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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| Vydané v: | International journal of adaptive control and signal processing Ročník 33; číslo 11; s. 1601 - 1618 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Bognor Regis
Wiley Subscription Services, Inc
01.11.2019
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| ISSN: | 0890-6327, 1099-1115 |
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| 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. |
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| AbstractList | 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. 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. |
| Author | Zhang, Xiao Ding, Feng Xu, Ling |
| Author_xml | – sequence: 1 givenname: Feng orcidid: 0000-0002-2721-2025 surname: Ding fullname: Ding, Feng email: fding@jiangnan.edu.cn organization: Jiangnan University – sequence: 2 givenname: Xiao orcidid: 0000-0002-6413-6148 surname: Zhang fullname: Zhang, Xiao organization: Jiangnan University – sequence: 3 givenname: Ling orcidid: 0000-0002-5040-5634 surname: Xu fullname: Xu, Ling organization: Jiangnan University |
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This paper derives the input‐output representation of the dynamical system described by a linear multivariable state‐space model and the corresponding... This paper derives the input‐output representation of the dynamical system described by a linear multivariable state‐space model and the corresponding... |
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| SubjectTerms | Algorithms Convergence gradient search Identification Innovations Multivariate analysis multivariate system multi‐innovation identification Parameter estimation Regression analysis |
| Title | The innovation algorithms for multivariable state‐space models |
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