# Nonparametric identification of Wiener systems by orthogonal series

@article{Greblicki1994NonparametricIO, title={Nonparametric identification of Wiener systems by orthogonal series}, author={Włodzimierz Greblicki}, journal={IEEE Trans. Autom. Control.}, year={1994}, volume={39}, pages={2077-2086} }

A Wiener system, i.e., a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade, is identified. Both the input signal and disturbance are random, white, and Gaussian. The unknown nonlinear characteristic is strictly monotonous and differentiable and, therefore, the problem of its recovering from input-output observations of the whole system is nonparametric. It is shown that the inverse of the characteristic is a regression function and a class of…

## 133 Citations

### Nonparametric approach to Wiener system identification

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- 1997

A Wiener system, i.e., a system consisting of a linear dynamic subsystem followed by a memoryless nonlinear one is identified, and the results hold for any nonlinear characteristic, and any asymptotically dynamic subsystem.

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The authors prove convergence of the proposed identification algorithms and examine their convergence rates.

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Recursive algorithms to identify both subsystems of a continuous-time Wiener system are presented. The system is driven and disturbed by Gaussian white random signals. The impulse response of the…

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A new method for Wiener system identification that relies on the data collected on two separate experiments that shows that the estimation of the static nonlinearity reduces to the solution of a least squares problem and provides an expression for the asymptotic variance of the estimated polynomial coefficients.

### On Recursive parametric Identification of Wiener Systems

- MathematicsInf. Technol. Control.
- 2011

It is shown here that the problem of parametric identification of a Wiener system could be reduced to a linear parametric estimation problem by a simple input-output data reordering and by a following data partition.

### On the Identification of Wiener Systems Having Saturation-like Functions with Positive Slopes

- MathematicsInformatica
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It is shown here that by a simple data reordering and by a following data partition the problem of identification of a nonlinear Wiener system could be reduced to a linear parametric estimation problem.

### On nonparametric identification of cascade nonlinear systems

- Mathematics, Computer ScienceProceedings of 1994 33rd IEEE Conference on Decision and Control
- 1994

Systems consisting of linear dynamic and memoryless nonlinear elements are identified, including the Hammerstein and Wiener cascade models, and deconvolution procedures for recovering the nonlinearities are proposed using orthogonal series techniques.

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- MathematicsProceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)
- 2002

Wiener systems consist of a linear dynamic system whose output is measured through a static nonlinearity. In this paper we study the identification of single-input single-output Wiener systems with…

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