Identification of nonlinear discrete-time systems using raised-cosine radial basis function networks
International Journal of Systems Science
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International Journal of Knowledge-based and Intelligent Engineering Systems - Advanced Intelligent Techniques in Engineering Applications
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Neural Processing Letters
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Neural Processing Letters
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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 RBF that is smooth, yet has compact support. The RBF network coefficients are low-order polynomial functions of the input. A simple computational procedure is presented which significantly reduces the network training and evaluation time. Storage space is also reduced 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 continuous first derivative. When the network is used to approximate a nonlinear dynamic system, the resulting system is bounded-input bounded-output stable. For the special case of a linear system, the RBF network representation is exact 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 presented which illustrate the effectiveness of this technique