On the convergence speed of a class of higher-order ILC schemes

In iterative learning control (ILC) design, a direct objective is to achieve time-optimal learning in the presence of the system uncertainties. Higher-order ILC (HO-ILC) schemes have been proposed targeting at improving the convergence speed in the iteration domain. A m-th order ILC essentially uses system control information generated from past m iterations. A question is: can the convergence speed be improved in general by a HO-ILC? We show that, as far as the linear HO-ILC is concerned, the lower order ILC always outperform the higher-order ILC in the sense of time weighted norm. In order to facilitate a rigorous analysis of HO-ILC convergence speed and lay a fair basis for comparisons among ILC with different orders, the problem is formulated into a robust optimization problem in a min-max form