Robust convergence conditions of iterative learning control for time‐delay systems under random non‐repetitive uncertainties

Some of the most fundamental assumptions in the design of iterative learning control (ILC) for uncertain systems are the strict repetitiveness (i.e. iteration‐independence) of uncertainties in all factors of plant dynamic, external disturbances, initial conditions, and reference trajectory, which may not always hold in practical applications. The simultaneous relaxation of all these assumptions is a challenging problem that has been addressed only for delay‐free systems. This problem is still open for time‐delay systems, especially when the time‐delay factor also has non‐repetitive (i.e. iteration‐dependent/varying) uncertainty. Hence, this study extends the problem of robust ILC for a class of time‐delay systems under nonrepetitive uncertainties in not only plant dynamic, external disturbances, initial conditions, and reference trajectory but also time‐delay. By using the ILC scheme introduced in this work, and based on the frequency domain analysis, it is shown that both monotonic convergence and boundedness of the expected tracking error can be achieved (in the sense of L2‐norm) when the non‐repetitiveness (i.e. iteration‐dependence) of all existing uncertainties from a random viewpoint are taken into account. The effectiveness of the proposed strategy is verified by two simulation examples.