Training ANFIS as an identifier with intelligent hybrid stable learning algorithm based on particle swarm optimization and extended Kalman filter

This paper proposes a novel hybrid learning algorithm with stable learning laws for Adaptive Network-based Fuzzy Inference System (ANFIS) as a system identifier. The proposed hybrid learning algorithm is based on the particle swarm optimization (PSO) for training the antecedent part and the extended Kalman filter (EKF) for training the conclusion part. Lyapunov stability theory is used to study the stability of the proposed algorithm. Comparison results of the proposed approach, PSO algorithm for training the antecedent part and recursive least squares (RLSs) or EKF algorithm for training the conclusion part, with the other classical approaches such as, gradient descent, resilient propagation, quick propagation, Levenberg–Marquardt for training the antecedent part and RLSs algorithm for training the conclusion part are provided. Moreover, it is shown that applying PSO, a powerful optimizer, to optimally train the parameters of the membership function on the antecedent part of the fuzzy rules in ANFIS system is a stable approach which results in an identifier with the best trained model. Stability constraints are obtained and different simulation results are given to validate the results. Also, the stability of Levenberg–Marquardt algorithms for ANFIS training is analyzed.