Local approximation of control systems using artificial neural networks

Abstract

In this paper we study the local approximation problem, i.e. given a certain type of control system described by a set of differential equations can we construct an artificial neural network of Hopfield type that is a local approximation (in a well defined sense) to the system? Fortunately the answer to this question is yes, under certain constraints. The solution depends on a coordinate transformation based on the Lie algebras of the system and network.