A learning approach to tracking in mechanical systems with friction

This note describes a novel learning control scheme for tracking periodic trajectories in mechanical systems with friction. It is based on the fact that the solution of the closed-loop system tends to be periodic in steady state. When the closed-loop system reaches the steady state, the proposed learning control scheme updates the control input. By doing this iteratively, the proposed learning control scheme eventually can drive the tracking error to zero. Neither the information of the system mass nor the parametric model for friction is required for successful tracking. In particular, the proposed learning control scheme can be implemented at cheap cost on a commercially available microprocessor. Furthermore, its generality is well supported through rigorous convergence analysis.