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IMA Journal of Mathematical Control and Information Advance Access originally published online on May 25, 2008
IMA Journal of Mathematical Control and Information 2008 25(3):367-392; doi:10.1093/imamci/dnn002
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Identification of MIMO Hammerstein systems with non-linear feedback

Dapeng Luo{dagger}

Center of Excellence, Eaton Corporation, 13100 East Michigan Avenue, Galesburg, MI 49053, USA

Alexander Leonessa{ddagger}

Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0238, USA

{dagger} Email: dapengluo{at}eaton.com

{ddagger} Corresponding author. Email: leonessa{at}vt.edu

Received on October 25, 2007; Accepted on January 20, 2008

Subspace identification algorithms are proposed in this paper for a class of multi-input multi-output (MIMO) discrete-time closed-loop Hammerstein systems. In particular, instrumental variable (IV) techniques are applied to solve the correlations between the input signals and the signals that are fed back into the system. An augmented IV identification approach is introduced to address a problem related to the application of the numerical efficient RQ decomposition algorithm to a rank-decreased correlation matrix. The contribution of this paper is to provide a unified approach to identify a class of non-linear closed-loop systems and solve the related numerical issues during the implementation. Analysis and numerical examples are presented to demonstrate the validity of the algorithms proposed in this paper.

Keywords: subspace identification; non-linear identification; instrumental variable.


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