Approximation of state-space trajectories by locally recurrent globally feed-forward neural networks

Authors:
Krzysztof Patan
Affiliations:
Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
Venue:
Neural Networks
Year:
2008

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Abstract

The paper deals with investigating approximation abilities of a special class of discrete-time dynamic neural networks. The networks considered are called locally recurrent globally feed-forward, because they are designed with dynamic neuron models which contain inner feedbacks, but interconnections between neurons are strict feed-forward ones like in the well-known multi-layer perceptron. The paper presents analytical results showing that a locally recurrent network with two hidden layers is able to approximate a state-space trajectory produced by any Lipschitz continuous function with arbitrary accuracy. Moreover, based on these results, the network can be simplified and transformed into a more practical structure needed in real world applications.