The learning convergence of High Dimension CMAC_GBF

High-dimension cerebellar model articulation controller with general basis function (CMAC_GBF) is developed and its learning convergence is also proved in this study. Up till now, the applications of CMAC are mainly used as controller or system identification (function mapping). Due to the guaranteed convergence and learning speed of CMAC, all the applications have shown good performance. But for high-dimensional mapping or control, it requires a lot of memories; the consequence is not able to use CMAC_GBF or to use enormous resources to complete its mission. When CMAC_GBF is employed, the necessary memory is growing exponentially with increasing input dimensions, and this slows down the learning speed or turns out to be impossible. In this project, S_CMAC_GBF (A simple structure for CMAC_GBF) is employed to realize high-dimension application ability. Two 6-input nonlinear systems are employed to demonstrate the learning performance and the required practical memories of S_CMAC_GBF in high-dimensional applications. Briefly, the learning convergence is also proved.