System Control using Z ‐numbers
Wen Yu, Raheleh Jafari · 2019
This chapter utilizes dual fuzzy equations and fuzzy differential equations (FDEs) to model uncertain nonlinear systems, where the coefficients are Z-numbers. It discusses the existence of solutions to the dual fuzzy equations and FDEs. This corresponds to the controllability problem of fuzzy control. Two types of neural networks, feed forward, and feed back networks, are used to approximate the solutions (control actions) to the dual fuzzy equations and FDEs. The main idea is to find appropriate weights of neural networks such that the output of the neural network approaches the desired output. A special neural network named the Bernstein neural network is used to approximate the solutions of the FDE. Modified gradient descent algorithms are used to train the neural networks. The chapter also presents several real applications to show the use of the fuzzy equation and the FDE with Z-number coefficients to design the fuzzy controller.