Prespecified-time Consensus Control for Second-order Multi-agent Systems with Disturbances

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 the condition of an undirected graph, a second-order distributed predefined-time observer was designed to ensure that each follower can accurately estimate the leader’s state information within a predefined time, while addressing the algebraic loop problem and reducing communication burden. By utilizing the system state error, a novel distributed predefined-time sliding surface was designed to effectively improve the system’s convergence speed. Furthermore, a predefined-time consensus distributed control protocol considering external disturbances was designed to ensure that the system state tracking error converges to zero within the predefined time. Additionally, by combining algebraic graph theory and Lyapunov theory, the predefined-time stability of the closed-loop system was proven, and an estimate of the upper bound of the stabilization time could be obtained even when the initial system state was unknown. Finally, numerical simulation comparison experiments were conducted to verify the effectiveness and feasibility of the proposed strategy and analytical conclusions. 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 exhibits superior convergence performance. Compared with fixed-time control strategies, the upper bound of the convergence time of the proposed strategy is independent of the initial states of the agents, depends only on a single time parameter, and is independent of the controller parameters, offering precise estimation of the convergence time, simpler setup, and lower conservatism.