Complex systems modeling using dynamic fuzzy neural networks

Presents a dynamic fuzzy neural network (DFNN) for complex systems modeling. Using PID operator input layers, the DFNN network can be adopted to directly represent nonlinear continuous-time dynamic processes of unknown order and structure. The rationale is based on the fact that under a certain condition a nonlinear dynamic system can be approximated by a nonlinear combination of PID operators or a nonlinear PID system through learning processes. The dynamic network architecture and the competitive and supervised learning algorithms are given. Numerical examples are provided to illustrate the approximating ability of the proposed network for the inverse modeling of pH-neutralization processes