Abstract
This article focuses on the problem of prescribed-time control for a class of uncertain nonlinear systems. First, a prescribed-time stability theorem is proposed by following the adaptive technology for the first time. Based on this theorem, a new state feedback control strategy is put forward by using the backstepping method for high-order nonlinear systems with unknown parameters to ensure the prescribed-time convergence. Moreover, the prescribed-time controller is obtained in the form of continuous time-varying feedback, which can render all system states converge to zero within the prescribed time. It should be noted that the prescribed time is independent of system initial conditions, which means that the prescribed time can be set arbitrarily within the physical limitations. Finally, two simulation examples are provided to illustrate the effectiveness of our proposed algorithm.