Exponential convergence of an iterative learning controller for time-varying nonlinear systems

This paper addresses the issue of convergence rates in the tracking problem for a class of time varying nonlinear systems, using a PD-like iterative learning algorithm. It is shown that, under certain sufficient conditions involving the tracking horizon and the system parameters, the controller guarantees exponential convergence-with respect to the iteration index k-of the infinity norm of the tracking error. As a particular case, a class of linear time-varying systems is also considered, and sufficient conditions leading to exponential convergence are derived. The theoretical analysis, confirmed by the simulation results, demonstrates that the tracking horizon plays a crucial role in the convergence rates of the learning process