Adaptive neural network architectures for nonlinear function estimation

Adaptive radial basis function neural networks have been implemented in process controllers and estimators to approximate nonlinear functions which characterize the model. This work merges concepts from the study of wavelets, multiresolution analysis, and adaptive control and estimation theory. Existing algorithms adapt weights associated with each basis function in a grid with fixed node spacing and a specified dilation. However, the function being estimated may have dominant frequencies which may not be ideally suited by the chosen dilation. An algorithm which allows for simultaneous adaptation of coefficients and dilation is presented and evaluated. An alternative strategy is presented which combines the advantages of multiresolution neural network architectures with the ability of adaptive estimation laws to deal with time-varying systems. The performance of this adaptive multiresolution network architecture is compared to the dilation adaptation algorithm