Algebraic Identification of MIMO SARX Models

  • Authors:

  • Laurent Bako;René Vidal

  • Affiliations:

  • Département Informatique et Automatique, Ecole des Mines de Douai, Douai, France 59508 and Center for Imaging Science, Johns Hopkins University, Baltimore, USA MD 21218;Center for Imaging Science, Johns Hopkins University, Baltimore, USA MD 21218

  • Venue:
  • HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
  • Year:
  • 2008

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Abstract

We consider the problem of identifying the parameters of a multiple-input multiple-output switched ARX model with unknown number of submodels of unknown and possibly different orders. This is a very challenging problem because of the strong coupling between the unknown discrete state and the unknown model parameters. We address this challenge by algebraically eliminating the discrete state from the switched system equations. This algebraic procedure leads to a set of hybrid decoupling polynomials on the input-output data, whose coefficients can be identified using linear techniques. The parameters of each subsystem can then be identified from the derivatives of these polynomials. This exact analytical solution, however, comes with an important price in complexity: The number of coefficients to be identified grows exponentially with the number of outputs and the number of submodels. We address this issue with an alternative scheme in which the input-output data is first projected onto a low-dimensional linear subspace. The projected data is then fit with a single hybrid decoupling polynomial, from which the classification of the data according to the generating submodels can be obtained. The parameters of each submodel are then identified from the input-output data associated with each submodel.