Periodic adaptive learning compensation of state-dependent disturbance

This study addresses an improved version of periodic adaptive learning compensation scheme of state-dependent disturbances. The main contribution of this paper is the relaxation of assumptions given by Ahn and Chen and the generalisation of the periodic adaptive learning compensation for a broad class of practical engineering applications. The results of this study are developed on the basis of Lyapunov stability analysis along the state domain, the so-called s-domain. The state-dependent disturbance is a function of position, and the position is repetitive as a unit mass is moving forward continuously and returns to the initial position. For the continuous forward moving in the first repetition, new control schemes are proposed. After the first repetitive trajectory, the authors ensure continuously forward moving, that is v(t)>0), of the system by satisfying a velocity requirement at a specified point along the trajectory.