Uniform Boundedness of Feedback Error Learning for a Class of Stochastic Nonlinear Systems

In this paper we analyze stochastic stability and boundedness of the neurophysiologically inspired feedback error learning (FEL) paradigm, a control algorithm that uses an inverse model of the plant to maximize tracking performance under uncertain conditions. FEL is analyzed in the framework of an adaptive state feedback controller. An inverse model of the plant is adaptively learned by a neural network based on basis functions, while the output of the feedback controller is used as the training signal. The nonlinear plant under consideration is described as a multidimensional SISO stochastic differential equation. The tracking error was shown to be uniformly bounded in the case where the variance of the noise on the parameter update rule was constant and the variance of the noise on the state variables was a function of the tracking error. When the system was allowed to have only noise on the states variables, with variance linear to the tracking error, then FEL was shown to be stochastically stable