An Elliptic Type‐2 Fuzzy CMAC With Time‐Varying Particle Swarm Optimization for Nonlinear Systems

This study aims to develop a new efficient neural network called Takagi–Sugeno–Kang fuzzy elliptic Type‐2 cerebellar model articulation controller (TSKFET2C) using improved particle swarm optimization for nonlinear systems. For identification and prediction problems, the TSKFET2C is used as the main identifier and the main predictor, respectively. The learning laws for the system parameters are established for all rules of the proposed structure based on the gradient descent algorithm and the minimization of the cost function. For the control problem, the TSKFET2C is used as the main controller, and an auxiliary controller is used to eliminate the residual error. The stability of the control system is guaranteed by Lyapunov theory. Moreover, an improved particle swarm optimization is employed to achieve optimal learning rates for updating the parameters of the TSKFET2C. Finally, the proposed TSKFET2C is applied to three types of nonlinear systems to illustrate its performance and effectiveness. Simulation results demonstrate that the proposed IPSO–TSKFET2C achieves significant accuracy, delivering lower root mean square error in two types of system identification and 4D hyperchaotic synchronization, while providing favorably competitive and robust performance in the prediction of the Henon map.