Controlling chaotic dynamical systems
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
Radial basis function and related models: an overview
Signal Processing
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Radial basis function networks for conversion of sound spectra
EURASIP Journal on Applied Signal Processing
IEEE Transactions on Signal Processing
Variable neural networks for adaptive control of nonlinear systems
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Radial basis function networks, regression weights, and the expectation-maximization algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
On the efficiency of the orthogonal least squares training method for radial basis function networks
IEEE Transactions on Neural Networks
Approximation of nonlinear systems with radial basis function neural networks
IEEE Transactions on Neural Networks
A Fast Fuzzy Neural Modelling Method for Nonlinear Dynamic Systems
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks
Global models for patient-ventilator interactions in noninvasive ventilation with asynchronies
Computers in Biology and Medicine
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Radial basis function networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs. Regularization techniques allow to define constraints on the smoothness of the curve by using the gradient of the function in the training. However, procedures that permit to arbitrarily set the value of the derivatives for the data are rarely found in the literature. In this paper, the orthogonal least squares (OLS) algorithm for the identification of RBFNs is modified to provide the approximation of a non-linear single-input single-output map along with its derivatives, given a set of training data. The interest in the derivatives of non-linear functions concerns many identification and control tasks where the study of system stability and robustness is addressed. The effectiveness of the proposed algorithm is demonstrated with examples in the field of data interpolation and control of non-linear dynamical systems.