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Optimality Analysis of the Two-Stage Algorithm for Hammerstein System Identification
Institut de Recherche en Informatique et Systèmes Aléatoires, France.
Peking University, China.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2009 (English)Report (Other academic)
Abstract [en]

The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least-squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2009. , 9 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2909
Keyword [en]
Nonlinear system identification
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-56070ISRN: LiTH-ISY-R-2909OAI: oai:DiVA.org:liu-56070DiVA: diva2:316870
Projects
CADICS
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-03Bibliographically approved

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Ljung, Lennart

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf