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Blind Identification of Polynomial Matrix Fraction for Disturbance Rejection
Robust Control Design, Volume # 7 | Part# 1
Authors
Tanaka, Daisuke; Hirotani, Takuya; Sugimoto, Kenji
Digital Object Identifier (DOI)
10.3182/20120620-3-DK-2025.00172
Page Numbers:
69-74
Index Terms
Identification for Robust Control; Robust Stability and Performance; Computational Methods
Abstract
This paper proposes an approach to blind system identification for disturbance rejection control. We first identify plant dynamics with unknown disturbance, based on a well-known FIR (Finite Impulse Response) approximation technique for BSD (Blind Signal Deconvolution) in terms of independence of signals. Since we are more interested in the system itself than signal deconvolution, we adopt polynomial matrix fraction with a given degree structure, and then adjust the coefficients by projecting the FIR learning law to this parameter space of modest dimension. Finally we design feedback control for disturbance rejection via the identified system representation. Numerical simulation for a simple example is carried out to illustrate the proposed approach.
References
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\bibitem[Cichocki et~al.(2002)Cichocki, and Amari]{CiAm:02}
A.~Cichocki and S.~Amari.
\newblock Adaptive Blind Signal and Image Processing, Learning Algorithms and Applications.
\newblock John Wiley \& Sons, LTD, 2002.
\bibitem[Hyvarinen et~al.(2001)Hyvarinen, Karhunen, and Oja]{HyKaOj:01}
A.~Hyvarinen, J.~Karhunen, and E.~Oja.
\newblock Independent Component Analysis.
\newblock John Wiley \& Sons, Inc, 2001.
\bibitem[Even et~al.(2007)Even, and Sugimoto]{EvSu:07}
J. Even and K. Sugimoto.
\newblock An ICA approach to semi-blind identification of strictly proper systems based on interactor polynomial matrix.
\newblock \emph{International Journal of Robust and Nonlinear Control}, Vol. 17, Issue 8, pages 752--768, 2007.
\bibitem[Nitta et~al.(2007)Nitta, and Sugimoto]{NiSu:07}
M. Nitta and K. Sugimoto.
\newblock Blind identification of polynomial matrix fraction via independent component analysis.
\newblock \emph{International Journal of Robust and Nonlinear Control}, Vol. 17, Issue 8, pages 732--751, 2007.
\bibitem[Nitta et~al.(2004)Nitta, and Sugimoto]{NiSu:04}
M.~Nitta and K.~Sugimoto.
\newblock A BSD Approach to Estimation and Suppression of Disturbance with Unknown Dynamics by H-infinity-Feedback.
\newblock \emph{IFAC Workshop on Adaptation and Learning in Control and Signal Processing (ALCOSP 04)}, 2004.
\bibitem[Zhang et~al.(2000)Zhang, and Cichocki]{ZhCi:00}
L.~Zhang and A.~Cichocki.
\newblock Blind Deconvolution of Dynamical Systems: A State-Space Approach.
\newblock \emph{J Signal Processing}, Vol. 4, No. 2, pages 113--130, 2000.
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