stability Properties of CMAC Neural Networks

The form of neural network called CMAC has been shown to have many characteristics well-suited to real time control problems. The CMAC structure can be implemented in hardware that is extremely fast, uses relatively few numbers of weights and trains more quickly than other forms of neural controllers. As yet, however, little has been reported in the literature concerning the stability characteristics of CMAC networks when used in feedback control systems. In this paper, stability of the CMAC network itself is analyzed in terms of a simplified linear model. The open-loop eigenvalues are shown to be functions of the network design parameters such as generalization, network size, and learning rate factor. The network is also analyzed in a simple closed-loop control system. While the results are not completely general, trends are exposed between rapid learning and closed-loop stability. The results are similar to the classic tradeoff between bandwidth and rise-time in all linear systems.