Identification using ANFIS with intelligent hybrid stable learning algorithm approaches and stability analysis of training methods

This paper proposes a novel hybrid learning algorithm with stable learning laws for Adaptive Network based Fuzzy Inference System (ANFIS) as a system identifier and studies the stability of this algorithm. The new hybrid learning algorithm is based on particle swarm optimization (PSO) for training the antecedent part and forgetting factor recursive least square (FFRLS) for training the conclusion part. Two famous training algorithms for ANFIS are the gradient descent (GD) to update antecedent part parameters and using GD or recursive least square (RLS) to update conclusion part parameters. Lyapunov stability theory is used to study the stability of the proposed algorithms. This paper, also studies the stability of PSO as an optimizer in training the identifier. Stable learning algorithms for the antecedent and consequent parts of fuzzy rules are proposed. Some constraints are obtained and simulation results are given to validate the results. It is shown that instability will not occur for the leaning rate and PSO factors in the presence of constraints. The learning rate can be calculated on-line and will provide an adaptive learning rate for the ANFIS structure. This new learning scheme employs adaptive learning rate that is determined by input–output data. Also, stable learning algorithms for two common methods are proposed based on Lyapunov stability theory and some constraints are obtained.