Recursive identification for multi-input–multi-output Hammerstein–Wiener system

ABSTRACT

In this paper, an identification method based on the recursive auxiliary variable least squares algorithm is proposed for a multi-input–multi-output Hammerstein–Wiener system with process noise. In the proposed identification method, the system is converted into the multivariate regression form under the condition that the nonlinear block in the output part is invertible. Then, the auxiliary variable is constructed, the parameters of the regression equations are identified, and the system parameter matrices can be obtained by matrix composition of the parameter product matrix. A theoretical analysis showed that the proposed method has uniform convergence when the process noise is white and has a finite variance. The effectiveness of the proposed method is validated through the experiments.

KEYWORDS:

• Hammerstein–Wiener system
• multi-input–multi-output
• uniform convergence
• auxiliary variable

Acknowledgments

We would like to thank the editor-in-chief, the associate editor and the anonymous reviewers for their careful reading of the manuscript and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61473072]; and the Science and Technology Development Plan of Jilin Province [grant number 20160312017ZX], [grant number 20170312031ZG].