Direct learning control of trajectories subject to high-order internal model for a class of continuous-time linear systems

Direct learning control (DLC) is a control method using pre-stored system information to determine the current system input. It has been applied in the case that the system plant is in somewhere similar to former systems, for example, in output reference trajectories. Therefore, new control input can be deduced directly from system information stored a priori according to the known relationship. In this paper, considering multiple time-varying unknown parameters, a DLC law is proposed for a class of continuous-time linear systems with non-repeatable problems. The previously control profiles which are generated for non-repeatable trajectories were stored in the system already. The newly given reference trajectory is correlated with the pre-stored reference trajectories in terms of high-order internal model (HOIM). It is shown by theoretic proof and illustrative example of single-link robot manipulator that DLC algorithm can be effectively applied to the tracking trajectory by making full use of the pre-stored control information directly.