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Approximation of nonlinear systems with radial basis function neural networks
R J Schilling1, J J Carroll, A F Al-Ajlouni
1Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY 13699-5720, USA.
IEEE Transactions on Neural Networks
|February 5, 2008
Summary
This study introduces a novel radial basis function (RBF) neural network technique for function approximation. The method enhances computational efficiency and reduces storage, proving effective for dynamic systems.
Area of Science:
- Computational mathematics
- Artificial intelligence
- Neural networks
Background:
- Function approximation is crucial in many scientific and engineering fields.
- Existing methods may face challenges with computational efficiency and storage requirements.
- Radial Basis Function (RBF) networks offer a powerful framework for approximation tasks.
Purpose of the Study:
- To present an efficient technique for approximating continuous functions using radial basis function (RBF) neural networks.
- To develop an RBF network with a smooth, compact support function for improved performance.
- To reduce computational time and storage space for function approximation.
Main Methods:
- Utilized an n-dimensional raised-cosine type of RBF with compact support.
- Developed a computational procedure to lower network training and evaluation times.
- Employed a nonuniform grid for RBF centers to minimize storage requirements.
Main Results:
- The RBF network coefficients are low-order polynomial functions of the input.
- Network output demonstrated continuity and a continuous first derivative.
- Approximation of nonlinear dynamic systems resulted in bounded-input bounded-output stability.
- Exact and optimal representation was achieved for linear systems.
Conclusions:
- The presented RBF neural network technique offers significant improvements in computational efficiency and storage.
- The method is effective for approximating continuous functions and dynamic systems.
- This approach provides an exact and optimal solution for linear system representation.
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