Open-closed-loop PD-type iterative learning controller for nonlinear systems and its convergence

Lots of iterative learning control (ILC) algorithms have been developed to improve tracking performance of systems that track same trajectory repetitively. In this paper, we use an open-closed-loop PD-type ILC scheme for the control of a class of nonlinear systems. Sufficient condition for guaranteeing the convergence of the learning scheme is given under a few reasonable assumptions, and then proved with linear operator theory. It is shown that the proportional coefficients of the ILC scheme is not a factor for guaranteeing the convergence, the condition is weaker than known results for similar ILC schemes.