State-space LPV model identification using kernelized machine learning

S.Z. Rizvi, J.M. Velni, F. Abbasi, R. Tóth, N. Meskin

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Abstract

This paper presents a nonparametric method for identification of MIMO linear parameter-varying (LPV) models in state-space form. The states are first estimated up to a similarity transformation via a nonlinear canonical correlation analysis (CCA) operating in a reproducing kernel Hilbert space (RKHS). This enables to reconstruct a minimal-dimensional inference between past and future input, output and scheduling variables, making it possible to estimate a state sequence consistent with the data. Once the states are estimated, a least-squares support vector machine (LS-SVM)-based identification scheme is formulated, allowing to capture the dependency structure of the matrices of the estimated state-space model on the scheduling variables without requiring an explicit declaration of these often unknown dependencies; instead, it only requires the selection of nonlinear kernel functions and the tuning of the associated hyper-parameters.

Original languageEnglish
Pages (from-to)38-47
Number of pages10
JournalAutomatica
Volume88
DOIs
Publication statusPublished - 1 Feb 2018

Funding

This work was made possible by the NPRP grant # NRPR 5-574-2-233 from Qatar National Research Fund (QNRF), a member of the Qatar Foundation. The statements made here are solely the responsibility of the authors. The material in this paper was partially presented at Proc. of the 1st IFAC Workshop on Linear Parameter-Varying Systems, October 7–9, 2015, Grenoble France. This paper was recommended for publication in revised form by Associate Editor Cristian R. Rojas under the direction of Editor Torsten Söderström.

Keywords

  • Kernels
  • Linear parameter-varying models
  • Nonparametric identification
  • Support vector machines

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