Normalized fractional adaptive methods for nonlinear control autoregressive systems

The trend of applying mathematical foundations of fractional calculus to solve problems arising in nonlinear sciences, is an emerging area of research with growing interest especially in communication, signal analysis and control. In the present study, normalized fractional adaptive strategies are exploited for automatic tuning of the step size parameter in nonlinear system identification based on Hammerstein model. The brilliance of the methodology is verified by mean of viable estimation of electrically stimulated muscle model used in rehabilitation of paralyzed muscles. The dominance of the schemes is established by comparing the results with standard counterparts in case of different noise levels and fractional order variations. The results of the statistical analyses for sufficient independent runs in terms of Nash-Sutcliffe efficiency, variance account for and mean square error metrics validated the consistent accuracy and reliability of the proposed methods. The proposed exploitation of fractional calculus concepts makes a firm branch of nonlinear investigation in arbitrary order gradient-based optimization schemes.