State-Periodic Adaptive Friction Compensation

This paper focuses on the adaptive friction compensation, where the friction is considered as a position-dependent disturbance. We consider the case when the desired trajectory is state (e.g., position) periodical which is of course also time periodical. The key idea of our approach is to use one trajectory past information along the state axis to update the current adaptation since the friction is state-periodic. The new method consists of two main steps: Firstly, in the first repetitive trajectory, an adaptive compensator is designed to guarantee the $\\\\ell_2$-stability of the overall system; and secondly, from the second repetitive trajectory and onwards, a state-periodic adaptive compensator is designed based on stored past state-dependent information. Rigorous stability analysis is presented with a simulation example.