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Robust iterative learning control for linear continuous systems with vector relative degree under varying input trail lengths and random initial state shifts

For linear continuous multiple‐input multiple‐output systems with vector relative degree, which operate repetitively with an input‐driven motion and a following autonomous motion over a finite time interval, this article proposes an iteratively moving average operator (IMAO) based D‐type iterative learning control (ILC) method to address the iteratively varying input trail lengths and random initial state shifts. The proposed ILC algorithm has a rectifying action to random initial state shifts at the designed initial time interval. From the terminal time of rectifying action to the end of control input, it makes the ILC tracking error convergent into a bounded range, the bound of which is proportional to the initial state shifts. Specifically, as the initial state shifts remain fixed, the ILC tracking error can be driven to zero at the relevant time interval along the iteration axis. An example manifests the validity of the proposed IMAO based D‐type ILC algorithm.