Discrete-time CMAC neural networks for control applications

The cerebellar model articulation controller (CMAC) neural network (NN) has advantages over fully-connected NNs due to its increased structure. Since almost all the implementations of CMAC NNs are done on a digital computer, the discrete-time implementation of CMACs is of great importance. This paper attempts to provide a comprehensive treatment of digital implementation of CMAC NNs in closed-loop control applications. The function approximation capabilities of the CMAC NN are first established and novel weight-update laws derived that guarantee the stability of the closed-loop system. The passivity properties of the CMAC under the specified tuning laws are examined and the relationship between passivity and closed-loop stability is derived. The utility of the CMAC NN in controlling a nonlinear system with unknown dynamics is demonstrated through numerical examples