Boundedness of estimator with an improved back propagation algorithm

This paper proposes a novel learning algorithm with a variable learning gain and a σ-modification term for a multilayered neural network. The learning gain is decided by the `Levenberg-Marquardt´ algorithm, which is a nonlinear least squares method. The boundedness of the weightings is shown from a viewpoint of the robust adaptive control theory and a relationship between data sizes and learning rates is considered. Furthermore, simple numerical simulations are presented to show the efficiency of the proposed learning algorithm