Solving Trajectory Tracking of High-Order Fully Actuated Systems by Iterative Learning Control

This paper addresses the trajectory tracking problem for both fully actuated and sub-fully actuated systems. To achieve this, we formulate the desired input for various closed-loop systems under both fully and sub-fully actuated conditions. We then employ the P-type Iterative Learning Control (PILC) law and analyze its convergence properties. Our analysis reveals that PILC behaves similarly to the Jacobi iteration method, making it suitable for fully actuated systems but requiring the realizability of reference trajectories in sub-fully actuated systems. Moreover, we propose an improved PILC law that incorporates the current system state. Numerical simulations demonstrate that this enhancement effectively mitigates the transient growth of error.