Elsevier

Automatica

Volume 33, Issue 6, June 1997, Pages 1133-1139
Automatica

Brief paper
Model quality evaluation in set membership identification

https://doi.org/10.1016/S0005-1098(97)00007-1Get rights and content

Abstract

Identification from corrupted input-output measurements of systems that do not necessarily belong to the model class used is investigated. This leads to a nonstandard set membership (SM) identification problem. The ‘goodness’ of different model classes is measured by the conditional radius of information, a generalization of the radius in standard SM identification theory, giving a measure of the minimal worst-case modeling error. Upper and lower bounds on the radius are derived for linearly parameterized model classes. Specific formulas for the upper and lower bounds are given for the case of H2 identification of exponentially stable systems in the presence of powerbounded noise. The bounds are shown to coincide with the conditional radius when the model space dimension is equal to the number of output measurements. An almost-optimal identification algorithm is derived, giving identification error within the range of the derived bounds.

References (21)

  • B.Z. Kacewicz et al.

    Conditionally optimal algorithms and estimation of reduced order models

    J. Complexity

    (1988)
  • B. Wahlberg et al.

    On approximation of stable linear dynamical systems using orthonormal functions

    Automatica

    (1996)
  • M. Canale et al.

    Model quality evaluation in identification for control

  • M. Canale et al.

    Model structure selection in identification for control

  • L. Giarré et al.

    SM system identification with approximated models

  • L. Giarre et al.

    Robust control oriented H identification with mixed perturbation models1

  • G. Goodwin et al.

    Quantifying the error in estimated transfer functions with application to model order selection

    IEEE Trans. Autom. Control

    (1992)
  • B.Z. Kacewicz et al.

    Optimality properties in finite sample l1 identification with bounded noise

    Int. J. Adaptive Control Sig. Process

    (1995)
  • B.Z. Kacewizc et al.

    Optimality of central and projection algorithms for bounded uncertainty

    Syst. Control Lett.

    (1986)
  • L. Lin et al.

    Uncertainty principles and identification n-widths for LTI and slowly varying systems

    IEEE Trans. Autom. Control

    (1994)
There are more references available in the full text version of this article.

Cited by (38)

  • Certified system identification: Towards distribution-free results

    2012, IFAC Proceedings Volumes (IFAC-PapersOnline)
  • Identification and validation of quasispecies models for biological systems

    2009, Systems and Control Letters
    Citation Excerpt :

    Recently, some validation methodology have been applied with success to biological systems, [26], where the predictive capability of the model has been used to validate the model. Along the lines of [9,27], we first validate the a priori assumptions on the system, and then, if the actual data explain the system, we check the quality of the identified model. This quality evaluation is performed on the basis of the prediction error.

  • On input design in ℓ <inf>∞</inf> conditional set membership identification

    2006, Automatica
    Citation Excerpt :

    Conditional set membership identification (Garulli, Vicino, & Zappa, 2000b; Giarré, Kacewicz, & Milanese, 1997; Kacewicz, 1999; Kacewicz, Milanese, & Vicino, 1988) is a line of research that falls into the broader area of robust identification.

  • Guaranteed non-asymptotic confidence regions in system identification

    2005, Automatica
    Citation Excerpt :

    However, few rigorous finite sample results exists for bootstrap methods. Similarly to set membership identification, e.g. Milanese and Vicino (1991), Bai, Tempo, and Cho (1995), Bai,Nagpal,and Tempo (1996), Vicino and Zappa (1996), Giarre’, Kacewicz, and Milanese (1997), Giarre’, Milanese, and Taragna (1997), Garulli, Vicino, and Zappa (2000) and Garulli, Giarre’, and Zappa (2002), LSCR returns regions for the true system parameter. However, unlike the typical setting in set membership identification, LSCR does not assume that the disturbances are deterministic or bounded.

  • Global non-asymptotic confidence sets for general linear models

    2005, IFAC Proceedings Volumes (IFAC-PapersOnline)
  • Error bounds for fir models in conditional set-membership identification

    2005, IFAC Proceedings Volumes (IFAC-PapersOnline)
View all citing articles on Scopus

This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Brett Ninness under the direction of Editor Torsten Söderström.

View full text