Dynamical Leaderless Consensus of Third Order Uncertain Multi-Agent Systems With Only Relative Position Measurements

This paper focuses on the leaderless consensus problem of third order multi-agent systems with parametric uncertainties over a directed graph, where the agents reach consensus on their positions and high order derivatives. We design a novel extended state reference model using only relative position information as the input. Then an adaptive tracking algorithm is proposed to track the reference model in the presence of parametric uncertainties. We focus on the dynamical consensus, and prove the prerequisite of consensus is that the directed graph has a directed spanning tree and the eigenvalues of the transformed system matrix needs to have negative real parts except for three zero eigenvalues. Numerical simulation results are given to verify the effectiveness of proposed control algorithms.