On Feedback-based Iterative Learning Control for Nonlinear Systems without Global Lipschitz Continuity

Contraction mapping method is widely used in the design and analysis of feed-forward type of iterative learning control (ILC) for a class of nonlinear dynamic systems that satisfy global Lipschitz continuity condition. However, many engineering systems are only locally Lipschitz continuous. Thus contraction mapping method is not directly applicable to such systems. This paper proposes a feedback-based ILC algorithm for a class of nonlinear systems that is only locally Lipschitz continuous. In the proposed feedback-based ILC, the feed-forward controller or ILC is designed using a standard contraction mapping technique with an appropriate convergence condition while the feedback control is designed to stabilize the nonlinear dynamic systems. A novel composite energy function is proposed to show that the proposed feedback-based ILC can work even with the input saturation. Simulation results illustrate the effectiveness of the proposed method.