Neural network generalization and system sensitivity in feedback control systems

A new framework for quantifying and analyzing the generalization ability of neural networks in control systems is presented. Rigorous definitions to quantify the generalization ability of a neural network in the context of system control are given. Utilizing these definitions, it is proved that a successfully trained neural network always generalize "well" to some extent. This dual property of a trained neural network provides further justification for neuro-control approaches, because the added benefit of generalization is now analytically assured. In addition, a method for estimating the extent to which a trained neural network will generalize is presented. The results of this work provide new tools for performance analysis of neural-control systems, and represents a first step towards a rigorous framework for performance-oriented analysis and synthesis of neural networks for control.