Consensus of Second-order Multi-agent Systems with Directed Networks Using Relative Position Measurements Only

This brief paper studies the consensus problem of second-order multi-agent systems when the agents' velocity measurements are unavailable. Firstly, two simple consensus protocols which do not need velocity measurements of the agents are derived to guarantee that the multi-agent systems achieve consensus in directed networks. Secondly, a key constant which is determined by the complex eigenvalue of the nonsymmetric Laplacian matrix and an explicit expression of the consensus state are respectively developed based on matrix theory. The obtained results show that all the agents can reach consensus if the feedback parameter is bigger than the key constant. Thirdly, the theoretical analysis shows that the followers can track the position and velocity of the leader provided that the leader has a directed path to all other followers and the feedback parameter is bigger enough. Finally, numerical simulations are given to illustrate the effectiveness of the proposed protocols.