Feedback higher-order iterative learning control for nonlinear systems with non-uniform iteration lengths and random initial state shifts

Abstract

For nonlinear discrete-time systems with non-uniform iteration lengths and random initial state shifts, this paper developed a feedback higher-order iterative learning control (ILC) approach. To compensate the absent information of last iteration caused by non-uniform iteration lengths, the tracking information in both iteration domain and time domain is included in ILC design with the help of higher-order control and feedback control, respectively, while the general ILC schemes just adopt the information in iteration domain. A sufficient condition based on the higher-order ILC gains is derived. It is guaranteed that as the iteration number goes to infinity, the asymptotic bound of tracking error is proportional to random initial state shifts in mathematical expectation sense. Specifically, as the expectation of initial state shifts is zero, the ILC tracking error can be controlled to zero along the iteration direction. Two examples with different initial conditions are provided to validate the proposed ILC approach.