Feedback-aided PD-type iterative learning control for time-varying systems with non-uniform trial lengths

In most implementations of iterative learning control (ILC) for trajectory tracking, it is usually required that the trial lengths of different iterations are uniform. However, this requirement may not always be ensured in practical applications. In this paper, a feedback-aided PD-type ILC design for time-varying systems with non-uniform trial lengths is proposed. Although the actual trial lengths are non-uniform, the designed update sequences provide uniform full-length signals for the update process. Meanwhile, information from the most recent valid iterations can be better used than the mechanisms that compensate with hypothesized data, such as zero. Their recursive generation also reduces the storage burden compared to search strategies. The feedback error signal can be additionally used as part of the correction term to improve the system performance compared to the traditional open-loop approaches. Under a deterministic model, the main convergence results are obtained by combining the lambda-norm technique with the inductive analysis approach. At last, a linear numerical simulation and a nonlinear single-joint robot simulation are performed, respectively, to show that the proposed design can achieve the asymptotic tracking of the desired trajectories for time-varying systems with non-uniform trial lengths.