Data driven local coordinates for multivariable linear systems and their application to system identification

Authors:
Tomas Mckelvey;Anders Helmersson;Thomas Ribarits
Affiliations:
Department of Signals and Systems, Chalmers University of Technology, SE-412 96 Göteborg, Sweden;Department of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden;Institute for Econometrics, OR and System Theory, Vienna University of Technology, Argentinierstrasse 8, 1040 Vienna, Austria
Venue:
Automatica (Journal of IFAC)
Year:
2004

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Abstract

In this paper we introduce a new parametrization for state-space systems: data driven local coordinates (DDLC). The parametrization is obtained by restricting the full state-space parametrization, where all matrix entries are considered to be free, to an affine plane containing a given nominal state-space realization. This affine plane is chosen to be perpendicular to the tangent space to the manifold of observationally equivalent state-space systems at the nominal realization. The application of the parametrization to prediction error identification is exemplified. Simulations indicate that the proposed parametrization has numerical advantages as compared to e.g. the more commonly used observable canonical form.