Robust Iterative Learning Control for 2-D Linear Nonrepetitive Discrete Systems With Iteration-Dependent Trajectory

Abstract

In the existing robust iterative learning control (ILC) for 2-D discrete systems, they typicallly require to satisfy a core hypothesis that the strict repetitiveness of tracking reference trajectory and system model should be satisfied. This paper first investigates the robustness and convergence of a P-type ILC law and a high-order ILC law for 2-D linear nonrepetitive discrete systems (LNDS) with arbitrarily bounded reference trajectory and iteration-dependent reference trajectory described by a high order internal model (HOIM) operator in iteration domain, respectively. It is theoretically proved by using the 2-D linear nonrepetitive inequalities that the ILC tracking error and the control input robustly converge to a bounded range, the bound of which depends continuously on the bounds of all the nonrepetitive uncertainties. If these uncertainties are progressively convergent along the iteration domain, a precise tracking on the 2-D reference trajectory can be achieved. Two illustrative examples are provided to demonstrate the validity of the presented ILC law. Additionally, some comparative result on the practical dynamical processes is given.INDEX TERMS 2-D linear discrete nonrepetitive systems (LNDS), 2-D linear nonrepetitive inequalities, iteration-dependent trajectory, robust iterative learning control.