The Applications of Fuzzy Differentiable Cerebellar Model Articulation Controller in Function Approximation

A new neural network structure known as the fuzzy differentiable Cerebellar Model Articulation Controller (FD_CMAC) was presented in this study. The FD_CMAC mentioned in this study involved embedding the differentiable functions (such as Gaussian function) into the hypercube of the receptive field space, thereby forming non-fixed values and differentiable blocks. In addition, in the network structure, the fuzzy inference engine was introduced to replace the index addressing matrix of the association memory. Additionally, the fuzzy membership function was adopted to describe the mapping of the physical memory. The new network structure not only retained the features of CMAC, but also adopted the differentiable characteristics. The traditional weight equipartition is no longer the only method in the learning mechanism. Instead, the steepest descent method was adopted to derive at optimized parameters or weight memory contents. Confirmed through the simulation results, the network structure proposed in this study was not only feasible, but also possessed good approximation effects and convergence performance.