For a class of second-order nonlinear systems subject to matched disturbances, this paper investigates preset-time establishment and subsequent high-precision maintenance, and proposes a time-varying sliding mode control method based on prescribed error evolution. First, a quintic prescribed error-evolution function satisfying smooth endpoint constraints is constructed to explicitly shape the error establishment process, thereby avoiding excessive transient control demand caused by directly injecting a large initial error into the closed loop. Then, a time-varying sliding variable is constructed around the error-evolution deviation, and a continuous control law is designed by combining a bounded nonlinear mapping with a distance-dependent scheduling gain, achieving coordination between preset-time establishment and input smoothness. The theoretical analysis proves that, under nominal conditions, the closed-loop system can complete the establishment exactly at the preset instant; in the presence of bounded matched disturbances, the system satisfies an explicit small-neighborhood estimate at the preset instant and maintains high precision thereafter. The simulation results show that the proposed method achieves timing-consistent state establishment under different preset establishment scenarios, and significantly reduces the control peak and total input variation, thereby effectively alleviating the risk of actuator saturation.
Yuan et al. (Sun,) studied this question.