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

• Published in: Communications in nonlinear science & numerical simulation Vol. 79; p. 104901
• Main Authors: Cheng, Songsong, Wei, Yiheng, Sheng, Dian, Wang, Yong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2019; Elsevier Science Ltd
• Subjects: Algorithms; Convergence; Fractional order difference; Interpolation; LMS algorithm; Nonlinear control; Nonlinear system identification; Nonlinear systems; Spline interpolation; Stability; System effectiveness; LMS algorithm; Stability; Fractional order difference; Spline interpolation; Nonlinear system identification
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.104901

•A universal spline interpolation method is utilized to model nonlinear block.•Convergence analysis of the proposed method is developed.•A modified way is developed to improve the proposed method. 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.