Leader-following consensus of multiple uncertain euler-lagrange systems with unknown dynamic leader

In this paper, we consider the leader-following consensus problem of uncertain Euler-Lagrange multi-agent systems. In comparison with existing results, the leader system is used to formulate both the reference trajectory and external disturbances, and the dynamics of the leader system contains unknown parameters. The current setting makes our problem formulation more realistic while at the same time, it poses significant technical challenges to the solvability of the problem. Inspired by the robust control approach and the adaptive control approach, we propose a novel adaptive distributed control law. It is shown that by the proposed control law, consensus of multiple uncertain Euler-Lagrange systems can be achieved in spite of unknown dynamic leader systems. Our main result is demonstrated by its exemplary application to cooperative control of a group of two-link robot arms.