Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics

In this paper, we discuss the finite-time consensus problem for leaderless and leader-follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader-follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. Rigorous proof is given by using Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.