2004 Fiscal Year Final Research Report Summary
Stochastic Subspace Identification Method and its Applications to Closed-Loop Identification
| Project/Area Number |
15560376
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Control engineering
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
KATAYAMA Tohru Kyoto University, Graduate School of Informatics, Professor, 情報学研究科, 教授 (40026175)
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| Co-Investigator(Kenkyū-buntansha) |
TAKABA Kiyotsugu Kyoto University, Graduate School of Informatics, Associate Professor, 情報学研究科, 助教授 (30236343)
TANAKA Hideyuki Kyoto University, Graduate School of Informatics, Assistant Professor, 情報学研究科, 助手 (90303883)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Subspace Methods / Stochastic Realization / Feedback Systems / Canonical Correlation Analysis / QR Decomposition / Outliers / Singular Value Decomposition |
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| Research Abstract |
The objective of this research is to develop stochastic realization methods for multivariate time-series and then to obtain some stochastic subspace identification algorithms for closed-loop systems. The following are the results of the research in the past two years.
1.In [1], we have developed a new stochastic realization algorithm using canonical correlation analysis(CCA), thereby deriving the forward innovation model by means of LQ decomposition in a Hilbert space generated by second order stationary stochastic processes. In [2], we have reviewed a method of computing the canonical correlations between the future and past of a stationary stochastic process, and also reviewed an application of conditional CCA to the realization of stochastic systems in the presence of exogenous inputs.
2.A book on stochastic realization is published [3] (in Japanese).
3.By combining the orthogonal decomposition (ORT)-based method and a weighted LQ decomposition, we have developed a subspace identificat
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ion method for a linear stochastic system subjected to observation outliers [4]. Outliers in observed output sequence are detected by busing the ORT-method and a simple scheme in robust statistics based on the median of residuals.
4.A subspace identification method for a continuous-time plant operating in closed-loop is developed in the framework of the joint input-output approach. We first obtain an equivalent open-loop problem by using the dual Youla parameterization of the plant, and then derived a delta-operator based IV-MOESP type subspace identification algorithm. Simulation studies by using a chemical plant model show the feasibility of the method [5].
5.In [6], a subspace identification method of identifying state space models of the plant and controller operating in a closed-loop by using the ORT method. We have also discussed the role o f input signals in closed-loop identification in detail. Since the obtained models are of higher order, a model reduction procedure called SR method is employed to get lower dimensional models.
6.By using the EM algorithm, we have developed a method of improving estimates of a state space model obtained by subspace identification methods in the presence of observation outliers [7]. The EM algorithm is initialized by two subspace identification methods : MOESP and ORT. Numerical examples show that the EM algorithm can monotonically improve the initial estimates obtained by subspace identification methods. Less
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