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Variance Aspects of L2 Model Reduction when Undermodeling - the Output Error Case
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2002 (English)Report (Other academic)
Abstract [en]

In this contribution, variance properties of L2 model reduction are studied. That is, given an estimated model of high order we study the resulting variance of an L2reduced approximation. The main result of the paper is showing that estimating a low order output error (OE) model via L2 model reduction of a high order model gives a smaller variance compared to estimating a low order model directly from data in the case of undermodeling. This has previously been shown to hold for FIR (Finite Impulse Response) models, but is in this paper extended to general linear OE models.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2002. , 14 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2405
Keyword [en]
Identification, Model reduction, Variance
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55858ISRN: LiTH-ISY-R-2405OAI: oai:DiVA.org:liu-55858DiVA: diva2:316679
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-10-02Bibliographically approved
In thesis
1. Variance Expressions and Model Reduction in System Identification
Open this publication in new window or tab >>Variance Expressions and Model Reduction in System Identification
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Although system identification is now a mature research field, some problems remain unsolved. Examples of unsolved or partly unsolved problems are; accuracy of subspace identification algorithms, identification via model reduction, identification for control, and identification of non-linear systems. Some problems that fall into these categories are studied in this thesis.

This thesis discusses variance expressions in system identification. In particular, variance expressions for reduced models are analyzed.

The topic of model reduction via system identification has received little attention during the years. To understand how the variance of a high order model affects the reduced model, a general expression for the variance of the low order model as a function of the reduction method used is derived. This allows the analysis of all model reduction methods that can be written as a minimization criterion, where the function to be minimized is twice continuously differentiable. Many methods can be studied using this approach. However, the popular method of model reduction by balanced truncation of states does not immediately fit into this framework.

Many unsolved problems in system identification may be studied with the use of bootstrap methods. This statistical tool, used to assess accuracy in estimation problems, may be adopted to a series of problems in system identification and signal processing. The thesis presents how bootstrap can be adopted in the prediction error framework. In addition, we demonstrate how bootstrap can be applied to problems of constructing condence regions with a simultaneous confidence degree and calculating the variance of undermodeled models.

The thesis briefly discusses how set membership identification and prediction error identification can be combined into a more robust estimate. Finally, insights into how model validation can be performed in a more user informative way are also given.

Place, publisher, year, edition, pages
Linköping: Linköping University, 2002. 192 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 730
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-98162 (URN)91-7373-253-2 (ISBN)
Public defence
2002-02-22, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Supervisors
Available from: 2013-10-09 Created: 2013-09-30 Last updated: 2013-10-09Bibliographically approved

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