Convergence analysis of iterative learning control with respect to Lebesgue-p norm

In this paper, a conventional PD-type iterative learning control strategy for linear time-invariant system to track unique desired trajectory is studied. In the study, the convergence of the iterative learning updating law is analyzed in the sense of Lebesgue-p norm by means of Hausdorff-Young inequality of convolution integral. In the analysis, it is shown that the convergence property depends on not only the derivative learning gain but also the proportional learning gain. The validity of the conclusion and the effectiveness of the proposed learning strategy are exhibited by numerical simulations.