EMRBF: a statistical basis for using radial basis functions for process control

Radial basis function (RBF) neural networks offer an attractive equation form for use in model-based control because they can approximate highly nonlinear plants and yet are well suited for linear adaptive control. We show how interpreting RBFs as mixtures of Gaussians allows the application of many statistical tools including the expectation maximisation (EM) algorithm for parameter estimation. The resulting EMRBF models give uncertainty estimates and warn when they are extrapolating beyond the region where training data was available