On the modelling of nonlinear dynamic systems using support vector neural networks

Though neural networks have the ability to approximate nonlinear functions with arbitrary accuracy, good generalization results are obtained only if t he structure of the network is suitably chosen. Therefore, selecting the 'b est' structure of the neural networks is an important problem. Support vect or neural networks (SVNN) are proposed in this paper, which can provide a s olution to this problem. The structure of the SVNN is obtained by a constra ined minimization for a given error bound similar to that in the support ve ctor regression (SVR). After the structure is selected, its weights are com puted by the linear least squares method, as it is a linear-in-weight netwo rk. Consequently, in contrast to the SVR, the output of the SVNN is unbiase d. It is further shown here that the variance of the modelling error of the SVNN is bounded by the square of the given error bound in selecting its st ructure, and is smaller than that of the SVR. The performance of the SVNN i s illustrated by a simulation example involving a benchmark nonlinear syste m. (C) 2001 Elsevier Science Ltd. All rights reserved.