Optimality of first-order ILC among higher order ILC

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 trace of the control error covariance matrix in the presence of a class of uncorrelated random disturbances. 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. That is, an optimal HO-ILC does not add to the optimality of standard first-order ILC in the sense of minimizing the trace of the control error covariance matrix. The system under consideration is a linear discrete-time varying systems with different relative degree between the input and each output.