Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems

Abstract

This paper deals with studying the asymptotical properties of multilayer neural networks models used for the adaptive identification of wide class of nonlinearly parameterized systems in stochastic environment. To adjust the neural network’s weights, the standard online gradient type learning algorithms are employed. The learning set is assumed to be infinite but bounded. The Lyapunov-like tool is utilized to analyze the ultimate behaviour of learning processes in the presence of stochastic input variables. New sufficient conditions guaranteeing the global convergence of these algorithms in the stochastic frameworks are derived. The main their feature is that they need no a penalty term to achieve the boundedness of weight sequence. To demonstrate asymptotic behaviour of the learning algorithms and support the theoretical studies, some simulation examples are also given.