Robust higher‐order ILC for non‐linear discrete‐time systems with varying trail lengths and random initial state shifts

This study addresses a robust iterative learning control (ILC) scheme for non‐linear discrete‐time systems in which both the trail lengths and the initial state shifts could be randomly variant in iteration domain. The proposed higher‐order ILC law guarantees that as the iteration number goes to infinity, the ILC tracking errors at the desired output trail period are bounded in mathematical expectation, and the bound of tracking errors is proportional to the random initial state shifts. Specifically, the ILC tracking errors in mathematical expectation can be driven to zero as the expectation of initial state shifts is zero. Two numerical examples are carried out to demonstrate the effectiveness of the proposed higher‐order ILC law.