Synchronization of Multi-Agent Systems (MASs) has the potential to benefit many technological
areas such as formation control for unmanned vehicles, cooperative adaptive
cruise control, and spacecraft attitude control. Information plays a crucial role in MASs:
in centralized approaches, a central node utilizes global information to achieve synchronization,
while in distributed approach agents only utilize local information, i.e. neighbors’
information. A big concern in MASs is the presence of parametric uncertainties
(unknown dynamics), which might require adaptive control gains instead of fixed control
gains.

This work thus provides a novel adaptive distributed control for MASs of heterogeneous
agents with unknown dynamics based on model reference adaptive control (MRAC).
We study both the synchronization of linear systems and the synchronization of Euler-
Lagrange (EL) systems. The implementation of this scheme is based on distributed
matching condition assumptions. We study such matching conditions both for the statefeedback
case and output-feedback case. Since all matching gains are unknown in view
of the unknown dynamics, the gains are adapted online via Lyapunov-based estimation.
The asymptotic convergence of the synchronization error is analytically proven
by introducing an appropriately defined Lyapunov function, and numerical examples
show the effectiveness of the approach. The practical advantage of the proposed distributed
MRAC is the possibility of handling unknown dynamics by simply exchanging
the states/output, and inputs with neighbors, without any extra auxiliary variables (distributed
observer) nor sliding mode. Because of the mutual dependence of control inputs,
well-posedness problems will arise in the presence of cyclic communication, if the inputs
are generated without a prescribed priority. In this work, we study such well-posedness
problems via parameter projection methods.