A robust iterative learning control for linear system with variable initial state and trail length

To address the variable initial state and trail length this paper first presents a robust PD-type open-closed-loop iterative learning control (ILC) law for a multiple-input-multiple-output (MIMO) linear discrete-time system. It is demonstrated that the convergence condition is dependent on the PD-type feed-forward learning gains, while an appropriate feedback learning gain can improve the ILC convergence performance. As a special case of PD-type open-closed-loop ILC law, P-type and D-type open-closed-loop ILC laws are deduced. The three developed ILC laws ensure that as the number of iterations approaches infinity, the expectation of ILC tracking error will be constrained within a limited range, where the boundary is proportional to the initial state variation. Through a numerical simulation, the effectiveness of the proposed ILC laws is illustrated.