IDENTIFICATION FOR WIENER SYSTEMS WITH INTERNAL NOISE* |
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Authors: | Qijiang Song Hanfu Chen |
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Institution: | (1) Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China |
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Abstract: | This paper considers identification of Wiener systems for which the internal variables and output are corrupted by noises.
When the internal noise is a sequence of independent and identically distributed (iid) Gaussian random variables, by the Weierstrass
transformation (WT) the system under consideration turns to be a Wiener system without internal noise. The nonlinear part
of the latter is nothing else than the WT of the nonlinear function of the original system, while the linear subsystem is
the same for both systems before and after WT. Under reasonable conditions, the recursive identification algorithms are proposed
for the transformed Wiener system, and strong consistency for the estimates is established. By using the inverse WT the nonparametric
estimates for the nonlinearity of the original system are derived, and they are strongly consistent if the nonlinearity in
the original system is a polynomial. Similar results also hold in the case where the internal noise is non-Gaussian. Simulation
results are fully consistent with the theoretical analysis.
*This research is supported by the National Natural Science Foundation of China under Grant No. 60221301. |
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Keywords: | Recursive identification stochastic approximation strong consistency Wiener system Weierstrass transformation |
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