Recursive Radial Basis Functions for Multivariable Function Approximation

In many proposed applications of neural networks for control the network acts as a static nonlinear map which approximates the input-output characteirstics of controlled systems, such as mechanical manipulators or chemical processes. It has been shown recently that the radial basis function method for multivariable function approximation can match or even outperform the networks in speed of learning and accuracy of approximation. The main argument for selecting neural networks over the radial basis functions is the high speed of execution that can be realised if they are implemented in parallel hardware. This paper shows that for a class of problems the radial basis function method can be executed recursively, thus achieving high speed through software means on standard serial computers.