Second-order Robust Consensus for Nonlinear Multi-agent Systems with Extended State Observer

This paper studies the distributed cooperative tracking problem for several typical second-order nonlinear uncertain multi-agent systems with bounded external and internal disturbances. In the first place, a distributed control algorithm is proposed for Von Der Pol oscillators which do not satisfy the Lipschitz condition by using extended state observer. In this case, the velocity measurements are not available for state feedback. Then the extended case when only absolute position and relative position measurements are available is studied, we develop the proposed algorithm by introducing distributed filter for each follower, and results shown that the state of follower converge to the time-varying leader. In addition, the consensus problem of a group of non-identical pendulums is studied and the distributed cooperative tracking can be achieved under the algorithm.