Neural networks as on-line approximators of nonlinear systems

The authors present an approximation theory perspective in the design and analysis of nonlinear system identification schemes using neural network and other online approximation models. The identification procedure considered is based on a discrete-time formulation. Depending on the location of the adjustable parameters, networks are classified into linearly and nonlinearly parametrized networks. Based on this classification, a unified procedure for modeling discrete-time dynamical systems using online approximators is developed. The proposed identification methodology guarantees stability of the overall system even in the presence of modeling errors, and upper bounds for the average output error are obtained in terms of the modeling error. Simulation studies are used to illustrate the results and to compare different approximation models