Using RBFs in a CMAC to prevent parameter drift in adaptive control

Abstract

A radial Basis Function Network (RBFN) works well as a nonlinear approximator in direct adaptive control, as long as the number of inputs is low. A Cerebellar Model Arithmetic Computer (CMAC) indexes basis functions efficiently and can handle many inputs, but is prone to adaptive-parameter drift and subsequent bursting. This paper proposes using overlapping RBFs inside a CMAC structure. Specifically the RBFs associated with past and future (predicted) CMAC cells on a CMAC layer are activated along with the currently indexed cell׳s RBF on that layer. The novel neural network structure achieves the computational efficiency of the CMAC, yet can avoid drift when RBF widths are wide enough. Simulation results with a pendulum compare the performance and robustness of CMAC, RBF, and the proposed RBFCMAC in both the disturbance-free case and with sinusoidal disturbance.