Prescribed-time sliding mode control for uncertain nonlinear systems based on periodic delayed feedback and disturbance observer.

This paper addresses the trajectory tracking control problem of nonlinear systems subject to uncertain disturbances by proposing a unified prescribed-time control framework integrating disturbance observation and performance constraints. First, a prescribed-time disturbance observer with smooth adaptive gains and a time-varying scaling function is designed to ensure that the disturbance estimation error converges within a prescribed time. Subsequently, a prescribed-time sliding mode surface incorporating periodic delay feedback and time-varying switching gains is constructed to enhance robustness and accelerate the convergence process. Furthermore, a performance constraint mechanism based on a logarithmic barrier function is introduced to guarantee that the tracking error strictly satisfies the prescribed time-varying performance bounds throughout the response. Lyapunov stability analysis shows that the closed-loop system achieves prescribed-time convergence while satisfying the prescribed transient and steady-state performance requirements. Simulation results on a third-order Van der Pol system and a two-link robotic manipulator validate the effectiveness of the proposed method in terms of convergence speed, tracking accuracy, robustness, and control input smoothness.