Stable Nonlinear System Identification Using Neural Network Models

Abstract

Several empirical studies have demonstrated the feasibility of employing neural networks as models of nonlinear dynamical systems. This paper presents a stability theory approach to synthesizing and analyzing neural network based identification schemes. First static network architectures are combined with dynamical elements in the form of stable filters to construct a type of recurrent network configuration which is shown to be capable of approximating a large class of dynamical systems. Identification schemes, based on neural network models, are then developed using the Lyapunov synthesis approach with the projection modification method. These identification schemes are shown to guarantee stability of the overall system, even in the presence of modeling errors.