On Higher-Order Iterative Learning Control Algorithm in Presence of Measurement Noise

Higher-Order Iterative Learning Control (HO-ILC) algorithms use past system control information from more than one past iterative cycle. This class of ILC algorithms have been proposed aiming at improving the learning efficiency and performance. This paper addresses the optimality of HO-ILC in the sense of minimizing the control error covariance matrix in the presence of measurement noise. It is shown that the optimal weighting matrices corresponding to the control information associated with more than one cycle preceding the current cycle are zero. Consequently, an optimal HO-ILC is automatically reduced to an optimal first-order ILC. The system under consideration is a linear discrete-time varying systems with different relative degree between the input and each output. Furthermore, a suboptimal second-order ILC is proposed for a class of nonlinear systems. Based on a numerical example, it is shown that a compatible suboptimal first-order ILC yields better performance than the proposed suboptimal second-order ILC algorithm.