Consensus with connectivity preservation of uncertain Euler-lagrange multi-agent systems

The consensus problem for multiple Euler-lagrange systems has been extensively studied under various assumptions on the connectivity of the communication graph. In practice, it is desirable to enable the control law the capability of maintaining the connectivity of the communication graph, thus achieving consensus without assuming the connectivity of the communication graph. We call such a problem as consensus with connectivity preservation. In this paper, we will consider solving this problem for multiple uncertain Euler-lagrange systems. By combining the adaptive control technique and potential function technique, we will show that such a problem is solvable under a set of standard assumptions. By employing different potential functions, our approach will also lead to the solution of such problems as rendezvous, and flocking.