Fuzzy-Evolution Computing Paradigm for Fractional Hammerstein Control Autoregressive Systems

In this study, a fuzzy-evolution computing paradigm is presented for parameter estimation of fractional Hammerstein control autoregressive (F-HCAR) systems by exploiting the knacks of global optimization strength of genetic algorithms (GAs). The definition of Grunwald–Letnikov fractional derivative is exploiting in standard HCAR system for the development of F-HCAR model. The system identification problem of F-HCAR model is constructed by defining a merit or fitness function using mean square error approximation between the actual and calculated parameters of F-HCAR models. The decision variables of F-HCAR models are determined by optimization of merit function with the knacks of global search with GAs for sundry scenarios on noiseless and noisy environment in the system dynamics. Comparison of results between estimated and predicted responses of F-HCAR systems endorsed the accurate, stable and robust performance fuzzy-evolutionary GAs. The statistical calculations for merit function on MSE, Nash–Sutcliffe efficiency and Theil inequality coefficient through cumulative distribution plots, boxplot illustrations, histograms and probability results of Weibull distribution further substantiated designed procedures of fuzzy evolutionary GAs for F-HCAR systems.