Modeling and Control Using Fuzzy Equations
Wen Yu, Raheleh Jafari · 2019
This chapter discusses more general dual fuzzy equations. In order to model an uncertain nonlinear system, fuzzy equations and dual fuzzy equations are used, which are in the form of linear-in-parameter. The uncertainty is represented by fuzzy numbers. For modeling, the fuzzy equation is initially transformed into a neural network. Then the normal gradient descent method is modified to train the fuzzy coefficients. With this modification, normal neural modeling methods are applied to uncertainty nonlinear system modeling with fuzzy equations. The approximation theories for crisp models are extended into fuzzy cases. The upper bounds of the modeling errors with fuzzy equations are estimated. The approximation theory of crisp models is successfully extended to fuzzy equation model. The new methods are validated with some benchmark examples. Some simulation results are provided to show the performance and effectiveness of the fuzzy control and modeling design methods with neural networks.