Adaptive motion coordination with an unknown reference velocity

We study a motion coordination problem where a group of agents is required to reach consensus while tracking a leader's sinusoidal reference velocity. We assume that the frequency of the reference velocity is available only to the leader. Building on an existing passivity-based internal model control design, we develop a decentralized two-time-scale adaptive control that estimates the unknown frequency information and achieves consensus of the group. We establish uniform asymptotic stability of the adaptive design using a two-time-scale averaging theory. Simulation results illustrate the effectiveness of the proposed control.