Nonlinear Dynamics

, Volume 48, Issue 3, pp 275–284 | Cite as

Instrumental variables approach to identification of a class of MIMO Wiener systems

Original Article


A new approach to identification of multi-input multi-output (MIMO) Wiener systems using the instrumental variables method is presented. It is assumed that static nonlinear elements are invertible and their inverse characteristics can be expressed or approximated by polynomials of known orders. It is also assumed that the linear part of the Wiener system can be represented by a matrix polynomial form. Based on these assumptions, the Wiener system is transformed introducing a new parameterization and its parameters are estimated using a linear-in-parameters model. To solve the problem of non-consistency of least squares parameter estimates, an instrumental variables method is employed. A numerical example is included to show the effectiveness and the practical feasibility of the presented approach.


Instrumental variables method Linear regression Multi-input multi-output nonlinear systems Nonlinear system identification Parameter estimation Wiener models 



discrete Fourier transform


instrumental variables


least squares


multi-input multi-output


power hydrogen


root mean square error


single-input single-output


signal-to-noise ratio


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Institute of Control and Computation EngineeringUniversity of Zielona GóraulZielona GóraPoland

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