Design of modified fractional adaptive strategies for Hammerstein nonlinear control autoregressive systems

Abstract

In this study, modified fractional least mean square (FrLMS) algorithms are formulated for parameter estimation of Hammerstein nonlinear control autoregressive system (HNCAR) by exploiting the fractional calculus concepts in weight adaptation mechanism of the algorithm. In modified FrLMS (MFrLMS) of first kind, forgetting factor is applied to exploit the strength of both standard LMS and FrLMS algorithms. The MFrLMS algorithm of second kind is based on single fractional weight adaptation term in cost function for finding the optimal values instead of considering both fractional and first derivative terms as in FrLMS approach. Performance analysis of the proposed methods are carried out on the basis of optimization ability to the true values of HNCAR system, and comparison is made in terms of accuracy, convergence and complexity. Reliability and effectiveness of the proposed scheme is validated through performance indices based on mean square error, variance account for and Nash Sutcliffe efficiency for sufficient large number of independent runs.