Control of unknown nonlinear dynamical systems using CMAC neural networks: structure, stability, and passivity

The cerebellar model articulation controller (CMAC) neural network (NN) has advantages over fully connected NNs due to its increased structure. This paper attempts to provide a comprehensive treatment of CMAC NNs in closed-loop control applications. The function approximation capabilities of the CMAC NN are first rigorously 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.