Initial Rectifying of a Sampled-Data Iterative Learning Controller

Abstract

This paper considers sampled-data iterative learning control for a class of nonlinear continuous-time systems with initial shifts. A conventional sampled-data learning algorithm is examined in the presence of an initial shift. An impulsive action is shown to be involved in the resultant input profile as the sampling period tends to zero, which indicates that the conventional learning algorithm may not be applicable to the non-zero initial shift case as the sampling period is too small. In this paper, the performance improvement is shown possible by adding an initial rectifying action and iterative output trajectories are guaranteed to converge to the desired trajectory over a specified time interval. Furthermore, as there exist variable initial shifts at the beginning of each cycle, the initial rectified learning algorithm could ensure the output trajectories to follow the desired trajectory with a specified error bound, proportional to the bound on the initial shifts.