An online gradient-based parameter identification algorithm for the neuro-fuzzy systems

Online gradient descent method has been widely applied for parameter learning in neuro-fuzzy systems. The success of the application relies on the convergence of the learning procedure. However, there barely have been convergence analyses on the online learning procedure for neuro-fuzzy systems. In this paper, an online gradient learning algorithm with adaptive learning rate is proposed to identify the parameters of the neuro-fuzzy systems representing the Mamdani fuzzy model with Gaussian fuzzy sets. We take the reciprocals of the variances of the Gaussian membership functions, rather than the variances themselves, as independent variables when computing the gradient with respect to the variance parameters. Subsequently, oscillation of the gradient value in the learning process can be avoided. Furthermore, some convergence results for this online learning scheme are studied. Finally, three numerical examples are provided to illustrate the performance of the proposed algorithm.