Locally recurrent neural networks

Abstract

Artificial neural networks provide an excellent mathematical tool for dealing with non-linear problems [18, 23, 77]. They have an important property according to which any continuous non-linear relation can be approximated with arbitrary accuracy using a neural network with a suitable architecture and weight parameters. Their another attractive property is the self-learning ability. A neural network can extract the system features from historical training data using the learning algorithm, requiring little or no a priori knowledge about the process. This provides the modelling of non-linear systems with a great flexibility [18, 19]. However, the application of neural networks to the modelling or fault diagnosis of control systems requires taking into account the dynamics of processes or systems considered. A neural network to be dynamic must contain a memory. The memory can be divided into a short-term memory and a long-term memory, depending on the retention time [117, 36, 118, 23]. The short-term memory refers to a compilation of knowledge representing the current state of the environment. In turn, the long-term memory refers to knowledge stored for a long time or permanently. One simple way of incorporating a memory into the structure of a neural network is the use of time delays, which can be implemented at the synaptic level or in the input layer of the network. Another important way in which the dynamics can be built into the operation of a neural network in a implicit manner is through the use of feedbacks. The are two basic methods of incorporating feedbacks to a neural network: local feedback at the level of a single neuron inside the network and global feedback encompassing the whole network. Neural networks with one or more feedbacks are referred to as recurrent networks. This chapter is mainly focused on locally recurrent networks. © 2008 Springer-Verlag Berlin Heidelberg.