LPV system identification using the matchable observable linear identification approach

P. Lopes Dos Santos, R. Romano, T. P. Azevedo-Perdicoulis, Daniel Rivera, J. A. Ramos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This article presents an optimal estimator for discrete-time systems disturbed by output white noise, where the proposed algorithm identifies the parameters of a Multiple Input Single Output LPV State Space model. This is an LPV version of a class of algorithms proposed elsewhere for identifying LTI systems. These algorithms use the matchable observable linear identification parameterization that leads to an LTI predictor in a linear regression form, where the ouput prediction is a linear function of the unknown parameters. With a proper choice of the predictor parameters, the optimal prediction error estimator can be approximated. In a previous work, an LPV version of this method, that also used an LTI predictor, was proposed; this LTI predictor was in a linear regression form enablin, in this way, the model estimation to be handled by a Least-Squares Support Vector Machine approach, where the kernel functions had to be filtered by an LTI 2D-system with the predictor dynamics. As a result, it can never approximate an optimal LPV predictor which is essential for an optimal prediction error LPV estimator. In this work, both the unknown parameters and the state-matrix of the output predictor are described as a linear combination of a finite number of basis functions of the scheduling signal; the LPV predictor is derived and it is shown to be also in the regression form, allowing the unknown parameters to be estimated by a simple linear least squares method. Due to the LPV nature of the predictor, a proper choice of its parameters can lead to the formulation of an optimal prediction error LPV estimator. Simulated examples are used to assess the effectiveness of the algorithm. In future work, optimal prediction error estimators will be derived for more general disturbances and the LPV predictor will be used in the Least-Squares Support Vector Machine approach.

Original languageEnglish (US)
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4626-4631
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - Jan 18 2018
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: Dec 12 2017Dec 15 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Other

Other56th IEEE Annual Conference on Decision and Control, CDC 2017
CountryAustralia
CityMelbourne
Period12/12/1712/15/17

ASJC Scopus subject areas

  • Decision Sciences (miscellaneous)
  • Industrial and Manufacturing Engineering
  • Control and Optimization

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  • Cite this

    Dos Santos, P. L., Romano, R., Azevedo-Perdicoulis, T. P., Rivera, D., & Ramos, J. A. (2018). LPV system identification using the matchable observable linear identification approach. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 4626-4631). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8264342