Adaptive consensus for second-order uncertain multi-agent systems under a directed graph

In this paper, we study the consensus problem for second-order multi-agent systems under a directed graph where there exist parametric uncertainties in the agent dynamics. A distributed control algorithm relying on the relative position and velocity measurements is proposed for each agent. The agents achieve consensus with a common final constant velocity under the condition that the associated graph contains a directed spanning tree and the control gain is above some certain lower bounded, which are the same as the case of double integrators. The consensus convergence is analyzed via Lyapunov stability theory and input-to-state stability. Simulation results are provided to illustrate the effectiveness of the proposed algorithm.