Wavelet Amendment of Polynomial Models in Hammerstein Systems Identification

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A new wavelet algorithm for <emphasis emphasistype="boldital">on-line</emphasis> improvement of an existing polynomial model of nonlinearity in a Hammerstein system is proposed and its properties are examined. The algorithm employs wavelet bases on interval. Convergence of the resulting assembly, comprising the parametric polynomial model and a nonparametric wavelet add-on, to the system nonlinearity is shown. Rates of convergence for uniformly smooth and piecewise smooth nonlinearities with discontinuities are both established. </para>