A New Multilayer Takagi Sugeno Kang Elliptic Type- 2 Fuzzy Cerebellar-Imitated Neural Network for Nonlinear Systems Using Modified Grey-Wolf Algorithm

This paper aims to develop a new efficient multilayer neural network structure by combining the elliptic type-2 membership function with a Takagi- Sugenno-Kang (TSK) fuzzy system and a cerebellar model articulation controller to create a new multilayer TSK elliptic type-2 fuzzy cerebellar-imitated neural network (MTET2FCNN). The MTET2FCNN can be used as the main controller in the control problem, and it is also respectively used as the main identifier and predictor for identification and prediction problems. In addition, a modified Grey-Wolf optimization algorithm is used to update the optimal learning rates of the MTET2FCNN structure. System parameter learning is performed for all rules of the proposed MTET2FCNN structure based on the gradient descent algorithm and cost function minimization. The robust design of the compensator and the system's stability are proved by Lyapunov theory. The synchronization of a chaotic 4D Rabinovich system, the identification of a time-varying system, and a Mackey-Glass time series prediction demonstrate the performance and effectiveness of the proposed system.