Identification for Hammerstein nonlinear systems based on universal spline fractional order LMS algorithm

摘要

In this paper, we investigate the identification problem of the Hammerstein nonlinear systems. In order to approximate the nonlinear block and for the convenience of analyzing the convergence of the proposed algorithm, we modify the conventional spline interpolation such that the nonlinear output signal can be expressed in a universal form. Besides, we develop a fractional order LMS (Least-Mean-Square) algorithm to identify the linear block and control points of the nonlinear block and establish the convergence properties of the algorithm by employing the stability theory of fractional order difference systems. Finally, we also provide two numerical examples to illustrate the effectiveness of the proposed algorithm. (C) 2019 Elsevier B.V. All rights reserved.