Identification of Dynamical Systems Using Recurrent High-Order Neural Networks

Abstract

The use of multilayer neural networks for pattern recognition and for modeling of “static” systems is currently well-known (see, for example, [1]). Given pairs of input-output data (which may be related by an unknown algebraic relation, a so-called “static” function) the network is trained to learn the particular input-output map. Theoretical work by several researchers, including Cybenko [16], and Funahashi [24], have proven that, even with one hidden layer, neural networks can approximate any continuous function uniformly over a compact domain, provided the network has a sufficient number of units, or neurons. Recently, interest has been increasing towards the usage of neural networks for modeling and identification of dynamical systems. These networks, which naturally involve dynamic elements in the form of feedback connections, are known as recurrent neural networks.