Backstepping control for a two-link manipulator with appointed-time convergence

In this paper, a novel backstepping control law is investigated, which guarantees appointed-time convergence for a two-link manipulator. In contrast to other fixed-time controllers or predefined-time controllers, the practical convergence time can be precisely obtained instead of being estimated. By utilizing a novel appointed-time prescribed performance function, the trajectory tracking error of the manipulator can be previously constrained. Furthermore, the external disturbances have been suppressed by introducing a disturbance observer with the convergence time as a prior control parameter and a switching sliding mode control law. The stability of the controller is analyzed by the Lyapunov method. Various numerical simulation results are carried out to demonstrate the efficacy of the proposed control scheme.