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On-line wavelet estimation of Hammerstein system nonlinearity

Przemysław Śliwiński — 2010

International Journal of Applied Mathematics and Computer Science

A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlinearities and the rate of this convergence are both established.

A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

Przemysław ŚliwińskiZygmunt HasiewiczPaweł Wachel — 2013

International Journal of Applied Mathematics and Computer Science

A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewiseLipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output...

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