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In this paper, we study the leader-following consensus problem of multiple Euler-Lagrange (EL) 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 EL systems to be solved even if none of the followers knows the system matrix of the leader system exactly.

Adaptive Leader-Following Consensus for Multiple Euler–Lagrange Systems With an Uncertain Leader System