Convergence Analysis in the Sense of Lebesgue-p Norm for Open-Closed-Loop Iterative Learning Control

In this paper, a PD-type open-closed-loop iterative learning control strategy is studied for linear time-invariant system. By means of Hausdorff-Young inequality of convolution integral, the convergence of the proposed open-closed-loop iterative learning control updating law is analyzed for a given system in the sense of Lebesgue-p norm. It is shown from the theoretical analysis that the sufficient condition for convergence in sense of Lebesgue-p norm is dominated by not only the derivative learning gains but also the proportional learning gains. A comparable conclusion is theoretically discussed and the advantage of the updating law is numerically simulated.