Weighted consensus for multiple Lagrangian systems under a directed graph without using neighbors' velocity measurements

Motivated by the fact that the relative velocity information is difficult to obtain accurately, in this paper, we propose a leaderless consensus algorithm with gain adaptation for multiple Lagrangian systems without using neighbors' velocity information. By introducing an integral term in the auxiliary variable design, the final consensus equilibrium can be explicitly derived. We show that this equilibrium is dependent on three factors, namely, the interactive topology, the initial positions of the agents, and the control gains of the proposed control algorithm. We consider a nonsymmetric interactive topology where the associated graph is strongly connected. A Lyapunov-based method is presented to show the consensus convergence, where the input-to-state stability is used.