Brief paper: Two nonlinear optimization methods for black box identification compared

Authors:
Anne Van Mulders;Johan Schoukens;Marnix Volckaert;Moritz Diehl
Affiliations:
Vrije Universiteit Brussel, Department ELEC, Pleinlaan 2, B1050 Brussels, Belgium;Vrije Universiteit Brussel, Department ELEC, Pleinlaan 2, B1050 Brussels, Belgium;K.U.Leuven, Department MECH, Celestijnenlaan 300b, B3001 Leuven, Belgium;K.U.Leuven, Department ESAT, Kasteelpark Arenberg 10, B3001 Leuven, Belgium
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

In this paper, two nonlinear optimization methods for the identification of nonlinear systems are compared. Both methods estimate the parameters of e.g. a polynomial nonlinear state-space model by means of a nonlinear least-squares optimization of the same cost function. While the first method does not estimate the states explicitly, the second method estimates both states and parameters adding an extra constraint equation. Both methods are introduced and their similarities and differences are discussed utilizing simulation data. The unconstrained method appears to be faster and more memory efficient, but the constrained method has a significant advantage as well: it is robust for unstable systems of which bounded input-output data can be measured (e.g. a system captured in a stabilizing feedback loop). Both methods have successfully been applied on real-life measurement data.