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Zbl 1245.93134
Zhao, Wenxiao; Chen, Hanfu
Markov chain approach to identifying Wiener systems. (English)
[J] Sci. China, Inf. Sci. 55, No. 5, 1201-1217 (2012). ISSN 1674-733X; ISSN 1869-1919/e

Summary: 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.

MSC 2000:: *93E12 System identification (stochastic systems)
60J10 Markov chains with discrete parameter

Keywords: Wiener system; recursive identification; stochastic approximation; Markov chain; strong consistency

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