Approximation Property of the Modified Elman Network
摘要
A new type of recurrent neural network is discussed, which provides the potential for modelling unknown nonlinear systems. The proposed network is a generalization of the network described by Elman, which has three layers including the input layer, the hidden layer and the output layer. The input layer is composed of two different groups of neurons, the group of external input neurons and the group of the internal context neurons. Since arbitrary connections can be allowed from the hidden layer to the context layer, the modified Elman network has more memory space to represent dynamic systems than the Elman network. In addition, it is proved that the proposed network with appropriate neurons in the context layer can approximate the trajectory of a given dynamical system for any fixed finite length of time. The dynamic backpropagation algorithm is used to estimate the weights of both the feedforward and feedback connections. The methods have been successfully applied to the modelling of nonlinear plants.