An important research issue in RBF networks is how to determine the ganssian centers of the radial-basis functions. We investigate a technique that identifies these centers with carefully selected training examples, with the objective to minimize the network’s size. The essence is to select three very small subsets rather than one larger subset whose size would exceed the size of the three smal...

Abstract—the Active-disturbance rejection control (ADRC) has the advantage of strong robustness, antiinterference capability, and it does not rely on the accurate math model of controlled plant. But the parameter self-turning of ADRC isn’t as easy as PID controller because there are more parameters to turn in ADRC. In this paper the parameters are self-turning by the Radial Basis Function (RBF)...

This paper presents CONORBIT, a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions and is an extension of the ORBIT algorithm (Wild, Regis, and Shoemaker 2008). It...

Normalisation of the basis function activations in a Radial Basis Function (RBF) network is a common way of achieving the partition of unity often desired for modelling applications. It results in the basis functions covering the whole of the input space to the same degree. However, normalisation of the basis functions can lead to other effects which are sometimes less desirable for modelling a...

An important problem in engineering is the identification of nonlinear systems, among them radial basis function neural networks (RBF-NN) using Gaussian activation functions models, which have received particular attention due to their potential to approximate nonlinear behavior. Several design methods have been proposed for choosing the centers and spread of Gaussian functions and training the...

What is now known as the Gibbs phenomenon was first observed in the context of truncated Fourier expansions, but other versions of it arise also in situations such as truncated integral transforms and for different interpolation methods. Radial basis functions (RBF) is a modern interpolation technique which includes both splines and trigonometric interpolations as special cases in 1-D, and it g...

Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD)...

In this paper, a supervised technique for training radial basis function (RBF) neural network classifiers is proposed. Such a technique, unlike traditional ones, considers the class memberships of training samples to select the centers and widths of the kernel functions associated with the hidden neurons of an RBF network. The result is twofold: a significant reduction in the overall classifica...

In 1996 an Introduction to Radial Basis Function Networks was published on the web 2 along with a package of Matlab functions 3. The emphasis was on the linear character of RBF networks and two techniques borrowed from statistics: forward selection and ridge regression. This document 4 is an update on developments between 1996 and 1999 and is associated with a second version of the Matlab packa...

We present different training algorithms for radial basis function (RBF) networks and the behaviour of RBF classifiers in three different pattern recognition applications is presented: the classification of 3-D visual objects, highresolution electrocardiograms and handwritten digits.