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Selection of best orthonormal rational basis
KTH, Superseded Departments, Signals, Sensors and Systems.
KTH, Superseded Departments, Signals, Sensors and Systems.
KTH, Superseded Departments, Signals, Sensors and Systems.ORCID iD: 0000-0002-1927-1690
2000 (English)In: SIAM Journal on Control and Optimization, ISSN 03630129 (ISSN), Vol. 38, no 4, 995-1032 p.Article in journal (Refereed) Published
Abstract [en]

This contribution deals with the problem of structure determination for generalized orthonormal basis models used in system identification. The model structure is parameterized by a prespecified set of poles representing a finite-dimensional subspace of H2. Given this structure and experimental data, a model can be estimated using linear regression techniques. Since the variance of the estimated model increases with the number of estimated parameters, one objective is to find coordinates, or a basis, for the finite-dimensional subspace giving as compact or parsimonious a system representation as possible. In this paper, a best basis algorithm and a coefficient decomposition scheme are derived for the generalized orthonormal rational bases. Combined with linear regression and thresholding this leads to compact transfer function representations. The methods are demonstrated with several examples.

Place, publisher, year, edition, pages
2000. Vol. 38, no 4, 995-1032 p.
Keyword [en]
Algorithms, Control system analysis, Functions, Linear control systems, Mathematical models, Poles and zeros, Regression analysis, Best basis algorithms, Orthonormal basis functions, Structure determination, Identification (control systems)
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-55411OAI: oai:DiVA.org:kth-55411DiVA: diva2:471622
Note
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Control, 36, pp. 551-562; Wahlberg, B., System identification using Kautz models (1994) IEEE Trans. Automat. Control, 39, pp. 1276-1281; Wahlberg, B., Hannan, E.J., Parametric signal modelling using Laguerre filters (1993) Ann. Appl. Probab., 3, pp. 467-496; Wahlberg, B., MÀkilÀ, P., On approximation of stable linear dynamical systems using Laguerre and Kautz functions (1996) Automatica J. IFAC, 32, pp. 693-708; Walsh, J.L., Interpolation and approximation by rational functions in the complex domain (1960) 3rd Ed., Amer. Math. Soc. Colloq. Publ., 20. , American Mathematical Society, Providence, RI; Wickerhauser, M.V., (1994) Adapted Wavelet Analysis, from Theory to Software, , A. K. Peters, Boston; Young, T.Y., Huggins, W.H., Discrete orthonormal exponentials (1962) Proceedings of the National Electronics Conference, 18, pp. 10-18. , Chicago, IL NR 20140805Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2013-09-05Bibliographically approved

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