Preventing bursting in adaptive control using an introspective neural network algorithm

This paper presents a solution to the problem of weight drift, and associated bursting phenomenon, found in direct adaptive control. Bursting is especially likely to occur when systems are nonminimum phase or open-loop unstable. Standard methods in the literature, including leakage, e-modification, dead-zone, and weight projection, all trade off performance to prevent bursting. The solution presented here uses a novel introspective algorithm operating within a Cerebellar Model Arithmetic Computer (CMAC) neural network framework. The introspective algorithm determines an estimate of the derivative of error with respect to each weight in the CMAC. The local nature of the CMAC cell domains enables this technique, since this derivative can be calculated at the moment a cell is deactivated – based on the error within the cell׳s domain. If the derivative looks significant, the resulting weight change (due to a Lyapunov-stable adaptive update law) remains in the cell׳s memory. An insignificant derivative results in the weight change being discarded before the cell׳s next activation. The algorithm can prevent bursting without sacrificing performance, verified through an experiment with a (nonminimum phase) flexible-joint robot and a simulation of an (open-loop unstable) quadrotor helicopter.