Approximation of nonlinear systems with radial basis function neural networks

A technique for approximating a continuous function of n. variables with a radial basis function (RBF) neural network is presented. The method uses an n-dimensional raised-cosine type of that RBF is smooth, yet has compact su pport. The RBF network coefficients are low-order polynomial functions of t he input. A simple computational procedure is presented which significantly reduces the network training and evaluation time. Storage space is also re duced by allowing for a nonuniform grid of points about which the RBFs are centered. The network output is shown to be continuous and have a continuou s first derivative. When the network is used to approximate a nonlinear dyn amic system, the resulting system is bounded-input bounded-output stable. F or the special case of a linear system, the RBF network representation is e xact on the domain over which it is defined, and it is optimal in terms of the number of distinct storage parameters required. Several examples are pr esented which illustrate the effectiveness of this technique.