Giving CMAC Basis Functions a Tail in Order to Prevent Bursting in Neural-Adaptive Control

This work proposes a modification to the Cerebellar Model Articulation Controller (CMAC) for use in a direct adaptive control scheme. With the original CMAC, when an oscillation in the input occurs between two CMAC cells and across the origin, the weights in the adjacent cells drift in opposite directions-resulting in control signal chatter. When the chatter is severe it can cause a sudden increase in error referred to as bursting. Weight update modifications strong enough to prevent weight drift can severely limit performance. In the proposed method each basis function has a tail, remaining non-zero for the duration of the subsequent cells indexing. A small oscillation about the origin now occurs entirely within each basis function, so that each weight is much less likely to drift in one direction. The robust weight modification can then be made much weaker, resulting in significantly better performance. A simulation of a quadrotor helicopter subject to both a sinusoidal disturbance and an unknown payload verifies the stability and performance of the proposed method.