Design of key term separated identification model for fractional input nonlinear output error systems: Auxiliary model based Runge Kutta optimization algorithm

Fractional calculus generalizes the conventional calculus to real order and become a popular tool for efficient modeling of complex engineering problems by providing better insight to the system through involving historical information. In this study, fractional calculus concepts are incorporated into input nonlinear output error (INOE) system and is generalized to fractional INOE (FINOE) model through Grunwald-Letnikov differential operator. The key-term-separation based identification model is presented to estimate the parameters of FINOE system that avoids the burden of identifying extra parameters due to cross product terms. The parameter estimation of systems modeled by Hammerstein output error structure is a challenging task, especially with incorporation of fractional concepts. An auxiliary model based Runge Kutta (RUN) optimization methodology is proposed for viable estimation of FINOE parameters by using the estimate for unmeasurable terms of information vector. The mean-square-error based fitness function is developed that minimizes the difference between the actual and estimated responses of the FINOE system. The efficacy of the proposed scheme is investigated in terms of convergence speed, computational cost, resilience, stability and correctness in approximation of accurate weights of the FINOE system for multiple noise variations. The superiority of the RUN for FINOE is endorsed via comparative analysis with 8 states of the arts in noisy environments.