Direct learning of control efforts for trajectories with different time scales

In this brief paper, we introduce a new learning control method: direct learning which is defined as the generation of the desired control input profile directly from existing control input profiles without any repeated learning. The motivation of developing direct learning control (DLC) schemes is to overcome the limitation of conventional learning control methods which require that the desired tracking patterns (trajectories) be strictly identical (repeatable) throughout the learning process. There are two main advantages of the direct learning control method. The first is that the learning control system is capable of fully utilizing the pre-stored control input signals which may correspond to tracking patterns with different time scales and be achieved through various control approaches. The second is the direct generation of the desired control input profile, thereafter it is possible to remove the whole iterative learning process. The focus of this paper is on direct learning of a class of nonperiodic trajectories which are identical in spatial distribution but different in time scales