On P-type iterative learning control for nonlinear systems without global Lipschitz continuity condition

One of fundamental postulates in iterative learning control (ILC) is that the dynamic system needs to be globally Lipschitz continuous (GLC). While numerous successful practical implementations of ILC for various applications have been reported in the literature, many engineered systems do not satisfy this condition. This indicates that the GLC condition may not be a necessary condition when designing an ILC algorithm for an engineered system. This work demonstrates this idea by using a simple P-type ILC updating law. It is shown that the P-type ILC is applicable to very general class of nonlinear dynamic systems with new proof techniques. Therefore, the new developments greatly complement and extend the existing results in the ILC literature. Simulation results demonstrate the effectiveness of the proposed method.