Informativity: how to get just sufficiently rich for the Identification of MISO FIR Systems with Multisine Excitation?

Kévin Colin (1) , Xavier Bombois (1) , Laurent Bako (1) , Federico Morelli (1)

1 MIS - Ampère, Département Méthodes pour l'Ingénierie des Systèmes

In Prediction Error Identification, the consistency of the identified parameter vector is only guaranteed if the data are informative enough i.e. if the excitation signal is sufficiently rich. For single-input single-output systems, one can verify whether a given excitation is sufficiently rich for a system based on the number of frequencies at which its power spectrum is nonzero. The extension of this criterion to multivariate systems is not straightforward. In the literature, one has proposed criteria based on the number of frequencies at which the power spectrum matrix of the excitation signal is strictly positive definite. However, this criterion is too restrictive as it does not cover the case of multisine excitations, while it is well known that such excitation signals can lead to consistent estimates. This paper proposes less restrictive conditions for the consistency of the identified parameter vector when FIR multiple-inputs single-output systems have to be identified with multisine signals in the open loop configuration.

Domaines: Automatique / Robotique

Kévin Colin, Xavier Bombois, Laurent Bako, Federico Morelli. Informativity: how to get just sufficiently rich for the Identification of MISO FIR Systems with Multisine Excitation?. 2019. ⟨hal-02070880v2⟩