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Variance computation for system matrices and transfer function from input/output subspace system identification

Szymon Gres 1 Michael Döhler 1 Laurent Mevel 1
1 I4S - Statistical Inference for Structural Health Monitoring
Inria Rennes – Bretagne Atlantique , COSYS - Département Composants et Systèmes
Résumé : The transfer function of a linear system is defined in terms of the quadruplet of matrices (A, B, C, D) that can be identified from input and output measurements. Similarly these matrices determine the state space evolution for the considered dynamical system. Estimation of the quadruplet has been well studied in the literature from both theoretical and practical points of view. Nonetheless, the uncertainty quantification of their estimation errors has been mainly discussed from a theoretical viewpoint. For several output-only and input/output subspace methods, the variance of the (A, C) matrices can be effectively obtained with recently developed first-order perturbation-based schemes. This paper addresses the estimation of the (B, D) matrices, and the remaining problem of the effective variance computation of their estimates and the resulting transfer function. The proposed schemes are validated on a simulation of a mechanical system.
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Submitted on : Monday, July 20, 2020 - 3:24:05 PM
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Szymon Gres, Michael Döhler, Laurent Mevel. Variance computation for system matrices and transfer function from input/output subspace system identification. IFAC 2020 - 21st International Federation of Automatic Control World Congress, Jul 2020, Berlin, Germany. ⟨10.1016/j.ifacol.2020.12.861⟩. ⟨hal-02902996⟩

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