Self-Organizing Radial Basis Function Network for Real-Time Approximation of Continuous-Time Dynamical Systems
- 26 February 2008
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Neural Networks
- Vol. 19 (3) , 460-474
- https://doi.org/10.1109/tnn.2007.909842
Abstract
Real-time approximators for continuous-time dynamical systems with many inputs are presented. These approximators employ a novel self-organizing radial basis function (RBF) network, which varies its structure dynamically to keep the prescribed approximation accuracy. The RBFs can be added or removed online in order to achieve the appropriate network complexity for the real-time approximation of the dynamical systems and to maintain the overall computational efficiency. The performance of this variable structure RBF network approximator with both Gaussian RBF (GRBF) and raised-cosine RBF (RCRBF) is analyzed. The compact support of RCRBF enables faster training and easier output evaluation of the network than that of the network with GRBF. The proposed real-time self-organizing RBF network approximator is then employed to approximate both linear and nonlinear dynamical systems to illustrate the effectiveness of our proposed approximation scheme, especially for higher order dynamical systems. The uniform ultimate boundedness of the approximation error is proved using the second method of Lyapunov.Keywords
This publication has 36 references indexed in Scilit:
- Variable neural networks for adaptive control of nonlinear systemsIEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews), 1999
- Performance evaluation of a sequential minimal radial basis function (RBF) neural network learning algorithmIEEE Transactions on Neural Networks, 1998
- Growing radial basis neural networks: merging supervised and unsupervised learning with network growth techniquesIEEE Transactions on Neural Networks, 1997
- Stable sequential identification of continuous nonlinear dynamical systems by growing radial basis function networksInternational Journal of Control, 1996
- Regularized orthogonal least squares algorithm for constructing radial basis function networksInternational Journal of Control, 1996
- Stable adaptive neural control scheme for nonlinear systemsIEEE Transactions on Automatic Control, 1996
- A perceptron network for functional identification and control of nonlinear systemsIEEE Transactions on Neural Networks, 1993
- Universal Approximation Using Radial-Basis-Function NetworksNeural Computation, 1991
- A Resource-Allocating Network for Function InterpolationNeural Computation, 1991
- Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systemsIEEE Transactions on Automatic Control, 1981