Anticipatory approach to design robust iterative learning control for uncertain time-delay systems

This paper is devoted to robust iterative learning control (ILC) design for time-delay systems (TDS) with uncertainties in both model plant and delay time. An ILC law is considered by using anticipation in time to compensate for the effects of delay, which has three design parameters: the weighting function, the lead time and the learning gain. For iteration-invariant TDS, it is shown that a necessary and sufficient condition can be obtained for the tracking error to converge for all admissible plant uncertainties. If the uncertainty is considered to be varying randomly from iteration to iteration, resulting in iteration-varying TDS, then a necessary and sufficient condition can be derived to ensure the convergence of the expected tracking error. For TDS in both cases, it is also shown that the convergence is monotonic in the sense of the ℒ₂-norm, and the estimated delay is sufficiently anticipatory for the selection of the lead time to achieve the robust ILC design. Simulation results are included to verify the theoretical study.