Auxiliary Model-Based Chameleon Swarm Optimization for Robust Parameter Estimation of Fractional Order Nonlinear Hammerstein Systems

Abstract Fractional calculus, an extension of traditional calculus to noninteger order, has become an influential tool for modeling complex engineering problems by incorporating historical data for better system understanding. This research investigates the parameter estimation of fractional Hammerstein output error (FHOE) systems by introducing an auxiliary model-based Chameleon swarm algorithm (CSA) that allows approximation of immeasurable terms present in the FHOE estimation model. The FHOE is constructed by integrating the Grunwald–Letnikov differential operator into the conventional Hammerstein output error system, and then a key-term separated identification scheme is offered for the FHOE model, effectively reducing the complexity of recognizing additional variables caused by cross-product relationships of linear and nonlinear blocks of the Hammerstein structure. A fitness function based on the mean square error is established to minimize the error between actual and estimated responses of the FHOE model. The efficiency of the presented auxiliary model-based CSA is established with respect to convergence speed, accuracy of estimated parameters, robustness, and stability for various noise and nonlinearity scenarios as compared with different counterpart algorithms.