Identification of fractional Hammerstein model for electrical stimulated muscle: An application of fuzzy-weighted differential evolution

Fractional order representations model complex systems with less parameters, improved accuracy and enhanced robustness in control systems but the system identification of fractional order systems is highly complicated and challenging task because of substantial nonlinearity of the input, unknown linear/nonlinear parameters of the blocks, and unknown fractional order. In this paper, parameter estimation technique is proposed based on fuzzy-weighted differential evolution algorithm for fractional electrically stimulated muscle models, which is generalization of fractional Hammerstein controlled autoregressive model vital for rehabilitation of spinal cord injury (SCI) patients. The system identification problem of fractional electrically stimulated muscle models (FESMMs) is formulated via mean square error approximation between the true and estimated response of FESMMs. The parameters of FESMMs are identified by employing fuzzy weighted differential evolution algorithm optimization knacks of with polynomial, cubic spline and sigmoidal input nonlinearities on various noise variances in the system dynamics. Comparison of results from actual to calculated responses indicates closeness up to 4 decimal places of accuracy for FESMM with polynomial type nonlinearity, up to 6 decimal places for FESMM with sigmoidal type kernel, and up to 5 decimal for FESMM with cubic spline type nonlinearity for different low and high signal to noise scenarios i.e., sigma(2)=0.002(2),0.02(2),0.2(2), which verify the precision, efficacy, stability and reliability of the fuzzy weighted differential evolution algorithm for system identification of FESMMs in rehabilitation scenarios of SCI.