On iterative learning control with high-order internal models

In this work we focus on iterative learning control (ILC) for iteratively varying reference trajectories which are described by a high-order internal models (HOIM) that can be formulated as a polynomials between two consecutive iterations. The classical ILC with iteratively invariant reference trajectories, on the other hand, is a special case of HOIM where the polynomial renders to a first-order internal model with a unity coefficient. By incorporating HOIM into the ILC law, and designing appropriate learning control gains, the learning convergence in the iteration axis can be guaranteed for continuous-time linear time-varying (LTV) systems. The initial resetting condition, P-type and D-type ILC, and possible extension to nonlinear cases are also explored in this work.