Stochastic stability of a neural‐net robot controller subject to signal‐dependent noise in the learning rule

Abstract

Abstract We consider a neural network‐based controller for a rigid serial link manipulator with uncertain plant parameters. We assume that the training signal to the network is corrupted by signal‐dependent noise. A radial basis function network is utilized in the feedforward control to approximate the unknown inverse dynamics. The weights are adaptively adjusted according to a gradient descent plus a regulation term (Narendra's e ‐modification). We prove a theorem that extends the Yoshizawa D‐boundedness results to the stochastic setting. As in the deterministic setting, this result is particularly useful for neural network robot control when there exists bounded torque disturbances and neural net approximation errors over a known compact set. Using this result, we establish bounds on the feedback gains and learning rate parameters that guarantee the origin of the closed‐loop system is semi‐globally, uniformly bounded in expected value. Copyright © 2009 John Wiley & Sons, Ltd.