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

*(English)*Zbl 1226.93014Summary: 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. A rigorous proof is given by using the Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method.

##### MSC:

93A14 | Decentralized systems |

94C15 | Applications of graph theory to circuits and networks |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

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