Abstract:
Aiming at the consensus control problem of second-order multi-agent systems with external disturbances, a distributed predefined-time control strategy based on sliding mode technology was proposed. Under undirected graph conditions, a second-order distributed predefined-time observer was designed to resolve the algebraic loop issue while reducing communication burden, and it was ensured that each follower could accurately estimate the leader’s state information within a predefined time. Using the system state error, a novel distributed predefined-time sliding surface was designed to improve the convergence speed effectively. Furthermore, a predefined-time consensus distributed control protocol considering external disturbances was designed to guarantee the system state tracking error convergence to zero within the predefined time. Additionally, through algebraic graph theory and Lyapunov theory, the predefined-time stability of the closed-loop system was rigorously proven, and the upper bound of the stabilization time was derived for unknown initial states. Finally, comparative numerical simulations verified the effectiveness and feasibility of the proposed strategy and theoretical analysis. The results show that compared with finite-time control strategies, the convergence time of the proposed strategy is independent of the system’s initial values and its convergence performance is proven superior, whereas against fixed-time control strategies, the upper bound of the convergence time is not only independent of the agents’ initial states and controller parameters but is solely determined by a single time parameter, with significant advantages of precise convergence time estimation, simplified parameter tuning, and reduced conservatism.