Two-time-scale adaptive internal model designs for motion coordination

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 a passivity-based control, we develop decentralized two-time-scale adaptive internal model control algorithms that estimate the unknown frequency information and achieve consensus of the group. We establish exponential stability of the algorithms using two-time-scale averaging theory. Simulation results with first order and second order agent dynamics illustrate the effectiveness of the proposed controls.