Design of Runge-Kutta optimization for fractional input nonlinear autoregressive exogenous system identification with key-term separation

Population-based metaheuristic algorithms have gained significant attention in research community due to its effectiveness in solving complex optimization problems in diverse fields. In this study, knacks of population-based Runge-Kutta optimizer (RUN) are exploited for the identification of fractional input non-linear exogenous auto-regressive (FINARX) system with key term separation. The fractional order calculus operator of the Grünwald-Letnikov derivative is exploited to develop FINARX from a conventional non-linear auto-regressive exogenous system. The identification scheme for FINARX model is implemented through a mean-square-error-based fitness function. RUN utilizes the slope variations calculated by the well-known Runge-Kutta method for an effective search mechanism in the exploration and exploitation phases. Moreover, an enhanced solution quality mechanism is employed for speedy convergence and keeping the movement toward the best solution by escaping the local optima. The robustness of the algorithm is analyzed by multiple variations of non-linearity as well as different noise scenarios. The performance of the RUN to identify the FINARX system is validated in terms of convergence rate, fitness value, robustness, and accuracy in weight estimation. The effectiveness of the RUN is further assessed through exhaustive simulations with their statistics as well as comparison with the standard recent counterparts, including the Whale optimization algorithm, Reptile Search algorithm, and Aquila optimizer on different performance indices for the FINARX system.