Integration of CMAC technique and weighted regression for efficient learning and output differentiability

Cerebellar model articulation controllers (CMAC) have attractive properties of learning convergence and speed. Many studies have used CMAC in learning control and demonstrated successful results. However, due to the fact that CMAC is a table lookup technique, a model implemented by a CMAC does not provide a derivative of its output. This is an inconvenience when using CMAC in learning structures that require such derivatives. This paper presents a new scheme that integrates the CMAC addressing technique with weighted regression to resolve this problem. Derivatives exist everywhere except on the boundaries of quantized regions. Compared with the conventional CMAC, the new scheme requires the same amount of memory and has similar learning speed, but provides output differentiability and more precise output. Compared with the typical weighted regression technique, the new scheme offers an efficient way to organize and utilize collected information.