Schilling R J, Carroll J J, Al-Ajlouni A F
Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY 13699-5720, USA.
IEEE Trans Neural Netw. 2001;12(1):1-15. doi: 10.1109/72.896792.
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.
提出了一种使用径向基函数（RBF）神经网络逼近n元连续函数的技术。该方法采用n维余弦型径向基函数，它既平滑又具有紧支集。径向基函数网络系数是输入的低阶多项式函数。给出了一个简单的计算过程，该过程显著减少了网络训练和评估时间。通过允许以径向基函数为中心的点的非均匀网格，存储空间也得以减少。网络输出被证明是连续的且具有连续的一阶导数。当该网络用于逼近非线性动态系统时，所得系统是有界输入有界输出稳定的。对于线性系统的特殊情况，径向基函数网络表示在其定义的域上是精确的，并且就所需不同存储参数的数量而言是最优的。给出了几个例子来说明该技术的有效性。
