NONLINEAR SYSTEM IDENTIFICATION VIA WAVELET EXPANSIONS

Abstract

Abstract: The paper deals with the problem of recovering a nonlinearity in a class of nonlinear dynamical systems of block-oriented structure.The class includes a large number of previously examined block-oriented models.The sought nonlinearity is allowed to have singular points like discontinuities and points of non-differentiability. In order to cope with such general nonlinearities the theory of wavelet expansions is applied. A major advantage of these expansions is adaptation to erratic behavior of the nonlinearity and local adaptation to the degree of smoothness of an unknown characteristic. Hence a wavelet-based identification algorithm of the nonlinearity is proposed and conditions for the convergence of the algorithm are given. For nonlinearities satisfying some smoothing conditions the rate of convergence is also evaluated