Consensus for second-order agent dynamics with velocity estimators via pinning control

A consensus problem is investigated for a group of second-order agents with an active leader where the velocity of the leader cannot be measured, and the leader as well as all the agents is governed by the same non-linear intrinsic dynamics. To achieve consensus in the sense of both position and velocity, a neighbour-based estimator design approach and a pinning-controlled algorithm are proposed for each autonomous agent. It is found that all the agents in the group can follow the leader, and the velocity tracking errors of estimators converge to zero asymptotically, without assuming that the interaction topology is strongly connected or contains a directed spanning tree. In terms of the switching topologies between the leader and the followers, similar results are obtained. Finally, these theoretical results are demonstrated by the numerical simulations.