Improved nonlinear Hebbian learning algorithm based on fuzzy cognitive networks model

Modeling and parameter identification problems based on fuzzy cognitive networks (FCN) is studied for a kind of nonlinear systems which is difficult to accurately modelled by the mechanism. First, fuzzy cognitive networks with numerical reasoning and fuzzy information expression is established. The FCN model can express the system utilizing the directed graph containing nodes, weights, and feedback. Second, due to the precision of the model depends on the weight parameter, a nonlinear Hebbian learning algorithm with terminal constraints is proposed. The algorithm introduces the actual feedback value of system to the process of weight training. Based on the old update mechanism, a correction term with difference between the feedback value and predictive value is increased, then normalized to the final weight iteration formula. This algorithm has the advantages of fast convergence rate, high accuracy. The nonlinear Hebbian algorithm solves the shortcomings of traditional nonlinear Hebbian learning algorithm that initial value is strongly depended. Finally, the proposed method is applied to water tank control system. The simulation results illustrate the nonlinear Hebbian learning algorithm based on FCN is effective. © 2016, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.