Fully Distributed Consensus for Second-order Uncertain Multi-agent Systems under a Directed Graph

In this paper, we study the leaderless consensus problem for second-order uncertain multi-agent systems with absolute velocity damping under a directed graph. A fully distributed algorithm is proposed, in which each agent uses only the relative position measurements with respect to its neighbors and its own absolute velocity damping. It turns out that all agents achieve consensus asymptotically with zero final velocities. The proposed algorithm is fully distributed in the sense that different agents use their own control gains. Based on a system transformation method and an auxiliary variable, the leaderless consensus problem for second-order uncertain multi-agent systems is converted into that for a first-order linear multi-agent system with a vanishing term. The consensus convergence is then analyzed via the Lyapunov stability theory and input-to-state stability. Numerical simulations are provided to verify the effectiveness of the proposed algorithm.