A novel nonlinear sliding mode control for predefined-time leader–following consensus based on distributed observer

This paper presents a novel nonsingular sliding-mode to realize predefined-time tracking control performance of Euler–Lagrange systems. The proposed algorithm integrates a predefined-time hierarchical control algorithm and an observer-based controller to achieve predefined-time stabilization. By incorporating the sliding-mode control strategy, dynamic uncertainties and external disturbances in the system can be effectively addressed, thereby enhancing its robustness. Furthermore, the application of the predefined-time hierarchical control algorithm ensures that the system reaches a stable state within a settling time while maintaining the smoothness of the control input. Based on the Lyapunov stability argument, some sufficient criteria for predefined-time stability are derived. Eventually, numerical simulations are proposed to demonstrate the effectiveness of the main theoretical methodology. This research provides an effective solution for the control of Euler–Lagrange systems.