Prescribed Error Performance Control for Second-Order Fully Actuated Systems

In this paper,the prescribed error trajectory control is proposed for second-order fully actuated systems.At first,by taking advantage of the full-actuation property,an intermediate control law is designed such that the intermediate closed-loop system is in a very simple form.Then,by utilizing the initial conditions of system states and the prescribed error performance function,the intermediate control law is developed to force the tracking error of the system on the proposed sliding mode surface from the beginning.The overall control law is obtained by combining the aforementioned steps.It is revealed that under the designed control law,the tracking error of the closed-loop system converges to zero along the prescribed error trajectory.Finally,an example is provided to validate the effectiveness of the presented approach.