Iterative learning control with high-order internal model for linear time-varying systems

In this work we focus on iterative learning control (ILC) for iteratively varying reference trajectories which are described by a high-order internal model. The high-order internal model (HOIM) is formulated as a polynomial 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 unity coefficient, in other words, the 0th order internal model. By inserting the polynomial (HOIM) into the past control input of 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 condition, P-type and D-type ILC, and possible extension to nonlinear cases are also explored.