This paper presents a novel fuzzy neural network structure for uncertain nonlinear systems based on the framework of cerebellar model neural network (CMNN) and the Takagi -Sugeno-Kang (TSK) fuzzy knowledge base. To solve the uncertainty problem of nonlinear systems better, the wavelet functions are used in the consequent parts of each TSK fuzzy rule instead of the linear combination of the input variables, and the Gaussian-type functions are used as the membership functions in the antecedent parts. Combining the advantages of the wavelet function, the CMNN and the TSK fuzzy system, this new model is more suitable for uncertain nonlinear systems. To provide rapid training, parameter update rules of the proposed model are derived based on the gradient descent method, in which the learning rates are online adapted. Furthermore the Lyapunov function is used to analyze the convergence of the considered systems. Finally, four different types of applications are applied to demonstrate the performance of the proposed model. The comparison simulation results with other models verify the effectiveness of this new model.

Holographic optical tweezers have unique non-physical contact and can manipulate and control single or multiple cells in a non-invasive way. In this paper, the dynamics model of the cells captured by the optical trap is analyzed, and a control system based on a novel self-organizing fuzzy cerebellar model neural network (NSOFCMNN) is proposed and applied to the cell manipulation control of holographic optical tweezers. This control system consists of a main controller using the NSOFCMNN with a new self-organization mechanism, a robust compensation controller, and a higher order sliding mode. It can accurately move the captured cells to the expected position through the optical trap generated by the holographic optical tweezers system. Both the layers and blocks of the proposed NSOFCMNN can be adjusted online according to the new self-organization mechanism. The compensation controller is used to eliminate the approximation errors. The higher order sliding surface can enhance the performance of controllers. The distances between cells are considered in order to further realize multi-cell cooperative control. In addition, the stability and convergence of the proposed NSOFCMNN are proved by the Lyapunov function, and the learning law is updated online by the gradient descent method. The simulation results show that the control system based on the proposed NSOFCMNN can effectively complete the cell manipulation task of optical tweezers and has better control performance than other neural network controllers.