Information matrix and D-optimal design with Gaussian inputs for Wiener model identification

• Kaushik Mahata ^[2] ; Johan Schoukens ^[1] ; Alexander De Cock ^[1]
  1. [1] Vrije Universiteit Brussel

     Vrije Universiteit Brussel

     Arrondissement Brussel-Hoofdstad, Bélgica

     
  2. [2] University of Newcastle, Australia
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 69, 2016, págs. 65-77
• Idioma: inglés
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• Resumen

  • We present a closed form expression for the Fischer’s information matrix associated with the identification of Wiener models. In the derivation we assume that the input signal is Gaussian. The analysis allows the linear sub-system in the Wiener model to have a generic rational transfer function of arbitrary order. It also allows the static nonlinearity of the Wiener model to be a polynomial of arbitrary degree. In addition, we show how this analysis can be used to design tractable algorithms for D-optimal input design. The idea is further extended to design optimal inputs consisting of a sequence of Gaussian signals with different mean values and variances. By combining Gaussian inputs with different means we can tune the amplitude distribution of the input to achieve the best identification accuracy in D-optimal sense. The analytical results are also illustrated with some numerical simulations.