Adaptive Consensus and Parameter Estimation of Multi-Agent Systems with An Uncertain Leader

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.