Feedforward neural networks have demonstrated an ability to learn arbitrary nonlinear mappings. Knowledge of such mappings can be of use in the identification and control of unknown or nonlinear systems. One such network, the Gaussian radial basis function (RBF) network has received a great deal of attention. Such networks, however, grow exponentially in size with the number of inputs. Several modifications to the standard RBF network are presented. A new network, the modified radial basis function (MRBF) network, which has far fewer adjustable parameters than its existing counterparts is proposed. The addition of recurrent weights to the MRBF network allows the network to learn dynamic mappings. Additionally, a new training algorithm based on gradient descent is developed for all of the parameters of the MRBF network. Simulations were performed which showed the new MRBF network was able to learn nonlinear systems as well as the standard RBF.
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