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

Abstract 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.