Dynamic optimal learning rates of a certain class of fuzzy neural networksand its applications with genetic algorithm

The stability analysis of the learning rate for a two-layer neural network (NN) Is discussed first by minimizing the total squared error between the a ctual and desired outputs for a set of training vectors. The stable and opt imal learning rate, in the sense of maximum error reduction, for each itera tion in the training (back propagation) process can therefore be found fur this two-layer NN, It has also been proven in this paper that the dynamic s table learning rate for this two-layer NN must be greater than zero. Thus i t is guaranteed that the maximum error reduction can be achieved by choosin g the optimal learning rate for the next training iteration. A dynamic fuzz y neural network (FNN) that consists of the fuzzy linguistic process as the premise part and the two-layer NN as the consequence part is then illustra ted as an immediate application of our approach, Each part of this dynamic FNN has its own learning rate for training purpose. A genetic algorithm is designed to allow a more efficient tuning process of the two learning rates of the FNN. The objective of the genetic algorithm is to reduce the search ing time by searching for only one learning rate, which is the learning rat e of the premise part, in the FNN. The dynamic optimal learning rates of th e two-layer NN can he found directly using our innovative approach, Several examples are fully illustrated and excellent results are obtained for the model car backing up problem and the identification of nonlinear first orde r and second order systems.