  In this paper, we study the leader-following consensus problem of multiple
Euler-Lagrange systems subject to an uncertain leader system. We first
establish an adaptive distributed observer for a neutrally stable linear leader
system whose system matrix is not known exactly. Under standard assumptions,
this adaptive distributed observer can estimate and pass the leader's state to
each follower through the communication network of the system without knowing
the leader's system matrix exactly. Under the additional assumption that the
leader's state is persistently exciting, this adaptive distributed observer can
also asymptotically learn the parameters of the leader's system matrix. On the
basis of this adaptive distributed observer, we further synthesize an adaptive
distributed control law to solve our problem via the certainty equivalence
principle. Our result allows the leader-following consensus problem of multiple
Euler-Lagrange systems to be solved even if none of the followers knows the
system matrix of the leader system exactly.
