While modern feedback controllers are based on linear models, many processes of concern to chemical engineers are non-linear. The models for these processes are often too complex for non-linear controller design, and their linearized counterparts may not adequately represent the process dynamics. Adaptive radial basis function neural networks have been implemented in process estimators and controllers to approximate non-linear functions that describe the process. Existing algorithms have been proposed which require specification of network properties such as dilation of the basis functions. This work demonstrates that the function representation may be improved by selection of an optimal dilation, and presents an algorithm that allows simultaneous adaptation of dilation and node weights. In order to deal with functions that may have more than one dominant dilation, a multiresolution network adaptation algorithm is proposed. Lyapunov stability is proven for both strategies, and performance is evaluated for the control of an exothermic CSTR.