RBF networks for nonlinear models subject to linear constraints

In this work, we present a study of nonlinear modelings based on RBF networks. The incorporation of prior knowledge in modelings is our specific concern for adding transparency and improving the performance of the networks. We focus on the prior knowledge within the class of linear constraints, which includes both linear equality and linear inequality constraints. Different with other existing modeling approaches using Lagrange multiplier technique, we propose a sub-model using the same RBF network configuration to impose the constraints. Two benefits are gained from this modeling approach in comparison with the conventional RBF networks. First, the transparency is added through a structural way with a higher degree of explicitness than an algorithm means. Second, on linear equality constraint problems, the proposed approach is able to obtain the learning solutions directly without involving iteration processes. Numerical results from three benchmark examples confirm the beneficial aspects on the proposed modeling approach.