Practical Prescribed-Time Control with Time Varying Gains for Nonlinear Systems

Abstract

Since convergence times of finite-time stabilization and fixed-time stabilization depend on the initial values, prescribed-time control plays a very significant role in practical applications. However, most of the existing control methods to achieve prescribed-time stabilization do not take the convergence accuracy into account. To this end, in this paper, a practical prescribed-time controller is proposed to guarantee that the tracking error of the nonlinear system can converge to prescribed accuracy within a prescribed time. Meanwhile, the convergence time is independent of the initial conditions. Combined with sliding mode control and time-varying gains, it is shown that the tracking error is guaranteed to be within the prescribed accuracy after the prescribed time. The developed control method is supported by some simulations of the tracking control of robot manipulator systems.