  In this note, the problem of simultaneous leader-following consensus and
parameter estimation is studied for a class of multi-agent systems subject to
an uncertain leader system. The leader system is described by a sum of
sinusoids with unknown amplitudes, frequencies and phases. A distributed
adaptive observer is established for each agent to estimate the unknown
frequencies of the leader. It is shown that if the signal of the leader is
sufficiently rich, the estimation errors of the unknown frequencies converge to
zero asymptotically for all the agents. Based on the designed distributed
adaptive observer, a distributed adaptive control law is synthesized for each
agent to solve the leader-following consensus problem.
