A converged recurrent structure for CMAC_GBF and S_CMAC_GBF

A new recurrent structure has been developed for both CMAC_GBF and S_CMAC_GBF in this paper. From the view of control, CMAC_GBF is capable of its excellent learning ability and superior of its control of complex nonlinear systems, but it is difficult for CMAC_GBF to solve problems of dynamic or time-relevant systems. This study develops recurrent structure for CMAC_GBF and S_CMAC_GBF with the method of employing the output of each hypercube to feedback to itself. This approach makes CMAC_GBF and S_CMAC_GBF to have the learning capability of temporal pattern sequences, and has more complex learning capability and is better than static feedforward networks. The design of recurrent structure and the driven of mathematic formulas and learning rules were accomplished in this paper. The proof of the learning convergence of the recurrent structure for CMAC_GBF and S_CMAC_GBF is completed. The examples of temporal pattern sequences will be demonstrated for the dynamic leaning capability of this recurrent structure.