Science China Information Sciences

, Volume 55, Issue 5, pp 1201–1217

Markov chain approach to identifying Wiener systems

Research Paper

DOI: 10.1007/s11432-012-4582-y

Cite this article as:
Zhao, W. & Chen, H. Sci. China Inf. Sci. (2012) 55: 1201. doi:10.1007/s11432-012-4582-y

Abstract

Identification of the Wiener system composed of an infinite impulse response (IIR) linear subsystem followed by a static nonlinearity is considered. The recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approximation algorithms with expanding truncations (SAAWET). With the help of properties of the Markov chain connected with the linear subsystem, all estimates derived in the paper are proved to be strongly consistent. In comparison with the existing results on the topic, the method presented in the paper simplifies the convergence analysis and requires weaker conditions. A numerical example is given, and the simulation results are consistent with the theoretical analysis.

Keywords

Wiener systemrecursive identificationstochastic approximationMarkov chainstrong consistency

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Key Laboratory of Systems and Control, Institute of Systems Science, AMSSChinese Academy of SciencesBeijingChina
  2. 2.National Center for Mathematics and Interdisciplinary SciencesChinese Academy of SciencesBeijingChina