  This paper studies the leaderless consensus problem of {heterogeneous}
multiple networked Euler-Lagrange systems subject to persistent disturbances
with unknown constant biases, amplitudes, initial phases, and frequencies. The
main characteristic of this study is that none of the agents has information of
a common reference model or of a common reference trajectory. Therefore, the
agents must simultaneously and in a distributed way: achieve consensus to a
common reference model (group model); achieve consensus to a common reference
trajectory; {and} reject the unknown disturbances. We show that this is
possible via a suitable combination of techniques of distributed `observers',
internal model principle, and adaptive regulation. The proposed design
generalizes recent results on group model learning, which have been studied for
linear agents over undirected networks. In this work, group model learning is
achieved for Euler-Lagrange dynamics over directed networks in the presence of
persistent unknown disturbances.
