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In this paper, we propose a non-parametric state-space identification approach for open-loop and closed-loop discrete-time nonlinear systems with multiple inputs and multiple outputs. Employing a least squares support vector machine (LS-SVM) approach in a reproducing kernel Hilbert space framework, a nonlinear auto-regressive model with exogenous terms is identified to provide a non-parametric estimate of the innovation noise sequence. Subsequently, this estimate is used to obtain a compatible non-parametric estimate of the state sequence in an unknown basis using kernel canonical correlation analysis. Finally, the estimate of the state sequence is used together with the estimated innovation noise sequence to find a non-parametric state-space model, again using a LS-SVM approach. The performance of the approach is analyzed in a simulation study with a nonlinear system operating both in open loop and closed loop. The identification approach can be viewed as a nonlinear counterpart of consistent subspace identification techniques for linear time-invariant systems operating in closed loop.

Original languageEnglish
Pages (from-to)1126-1131
Number of pages6
Issue number2
Publication statusPublished - 2020
Event21st World Congress of the International Federation of Aufomatic Control (IFAC 2020 World Congress) - Berlin, Germany
Duration: 12 Jul 202017 Jul 2020
Conference number: 21


  • Kernel canonical correlation Analysis
  • LS-SVM
  • NARX modeling
  • Nonlinear state-space Identification


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