A unified adaptive iterative learning control framework for uncertain nonlinear systems

In this note, we propose a unified framework for adaptive iterative learning control design for uncertain nonlinear systems. It is shown that if a Lyapunov based adaptive control law is available for the system under consideration and the Lyapunov function satisfies certain conditions, it is straightforward to extend the adaptive controller to handle repetitive systems operating over a finite time interval. According to the value of a certain parameter gamma, the parametric adaptation law can be a pure time-domain adaptation, a pure iteration-domain adaptation or a combination of both.(1) The advantages and disadvantages of the three possible adaptation types are discussed and some illustrative examples are given.