Iterative learning control for a class of nonlinear time-varying system

To a class of uncertain nonlinear time-varying systems with arbitrary initial states, we apply the method of rectifying desired trajectory to transform the problem of arbitrary initial states into the problem of varying desired trajectories with zero initial error. The computational procedures for obtaining the transition trajectories for the varying desired trajectories are presented. Then, a new iterative learning control (ILC) algorithm is developed for determining the varying desired trajectory, in which higher order derivatives of the desired trajectory is incorporated to handle the variations of the desired trajectory. A stable sliding-surface of tracking errors is designed to deal with the time-varying nonlinear uncertainty of the controlled system. The corresponding theorems are given in this paper and are proved in details by using the Lyapunov-like method. Simulation results validate the effectiveness of the proposed algorithm in which there is no need of the model structure information of the controlled system, thus extending the application scope of the adaptive ILC algorithm.