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In recent decades, fractional order calculus has become an important mathematical tool for effectively solving complex problems through better modeling with the introduction of fractional differential/integral operators; fractional order swarming heuristics are also introduced and applied for better performance in different optimization tasks. This study investigates the nonlinear system identification problem of the input nonlinear control autoregressive (IN-CAR) model through the novel implementation of fractional order particle swarm optimization (FO-PSO) heuristics; further, the key term separation technique (KTST) is introduced in the FO-PSO to solve the over-parameterization issue involved in the parameter estimation of the IN-CAR model. The proposed KTST-based FO-PSO, i.e., KTST-FOPSO accurately estimates the parameters of an unknown IN-CAR system with robust performance in cases of different noise scenarios. The performance of the KTST-FOPSO is investigated exhaustively for different fractional orders as well as in comparison with the standard counterpart. The results of statistical indices through Monte Carlo simulations endorse the reliability and stability of the KTST-FOPSO for IN-CAR identification. [ABSTRACT FROM AUTHOR]

Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is one of the most important approaches in ECP, which outperforms other standard approaches in terms of accuracy and convergence performance. In this study, a novel application of a recently proposed variant of DEA, the so-called, maximum-likelihood-based, adaptive, differential evolution algorithm (ADEA), is investigated for the identification of nonlinear Hammerstein output error (HOE) systems that are widely used to model different nonlinear processes of engineering and applied sciences. The performance of the ADEA is evaluated by taking polynomial- and sigmoidal-type nonlinearities in two case studies of HOE systems. Moreover, the robustness of the proposed scheme is examined for different noise levels. Reliability and consistent accuracy are assessed through multiple independent trials of the scheme. The convergence, accuracy, robustness and reliability of the ADEA are carefully examined for HOE identification in comparison with the standard counterpart of the DEA. The ADEA achieves the fitness values of 1.43 × 10−8 and 3.46 × 10−9 for a population size of 80 and 100, respectively, in the HOE system identification problem of case study 1 for a 0.01 nose level, while the respective fitness values in the case of DEA are 1.43 × 10−6 and 3.46 × 10−7. The ADEA is more statistically consistent but less complex when compared to the DEA due to the extra operations involved in introducing the adaptiveness during the mutation and crossover. The current study may consider the approach of effective nonlinear system identification as a step further in developing ECP-based computational intelligence. [ABSTRACT FROM AUTHOR]