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Robustness in identification and control pp 47–61Cite as

Semi-parametric methods for system identification

  • Part I Identification For Robust Control
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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 245))

Abstract

This paper is concerned with identification problems in general, structured interconnected models. The elements to be identified are of two types: parametric components and non-parametric components. The non-parametric components do not have a natural parameterization that is known or suggested from an analytical understanding of the underlying process. These include static nonlinear maps and noise models.

We suggest a novel procedure for identifying such interconnected models. This procedure attempts to combine the best features of traditional parameter estimation and non-parametric system identification. The essential ingredient of our technique involves minimizing a cost function that captures the “smoothness” of the estimated nonlinear maps while respecting the available input-output data and the noise model. This technique avoids bias problems that arise when imposing artificial parameterizations on the nonlinearities. Computationally, our procedure reduces to iterative least squares problems together with Kalman smoothing.

Our procedure naturally suggests a scheme for control-oriented modeling. The problem here is to construct uncertainty models from data. The essential difficulty is to resolve residual signals into noise and unmodeled dynamics. We are able to do this using an iterative scheme. Here, we repeatedly adjust the noise component of the residual until its power-spectral density resembles that supplied in the noise model. Our computations again involve Kalman smoothing. This scheme is intimately related to our procedure for semi-parametric system identification.

Finally, we offer illustrative examples that reveal the promise of the techniques developed in this paper.

Supported in part by an NSF Graduate Fellowship, by NASA-Dryden under Contract NAG4-124, and by NSF under Grant ECS 95-09539.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, 94720, Berkeley, CA

    Michiel Krüger, Eric Wemhoff, Andrew Packard & Kameshwar Poolla

Authors
  1. Michiel Krüger
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  2. Eric Wemhoff
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  3. Andrew Packard
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  4. Kameshwar Poolla
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Corresponding author

Correspondence to Kameshwar Poolla .

Editor information

A. Garulli (Assistant Professor)A. Tesi (Assistant Professor)

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© 1999 Springer-Verlag London Limited

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Krüger, M., Wemhoff, E., Packard, A., Poolla, K. (1999). Semi-parametric methods for system identification. In: Garulli, A., Tesi, A. (eds) Robustness in identification and control. Lecture Notes in Control and Information Sciences, vol 245. Springer, London. https://doi.org/10.1007/BFb0109859

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  • DOI: https://doi.org/10.1007/BFb0109859

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-179-5

  • Online ISBN: 978-1-84628-538-7

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