A discrete-time stochastic iterative learning control algorithm for a class of nonlinear systems

Abstract

This article presents a stochastic algorithm that computes the learning gain matrix of a “D-type iterative learning control (ILC) algorithm for a class of discrete-time varying nonlinear systems with linear input/output actions having relative degree one. The state disturbance, reinitialization errors, and measurement errors are considered to be zero-mean white processes. It is shown that the input error covariance matrix converges to zero in presence of uncorrelated disturbances. This algorithm does not require knowledge of the system dynamics or the disturbance statistics. The convergence rate of the input error covariance matrix is shown to be inversely proportional to the number of iterations. The author also shows that in presence of measurement noise, the state error covariance matrix converges to zero as the number of learning iterations increases. Finally, a numerical example is given that compares the performance of the proposed algorithm to a conventional ILC algorithm.