  This manuscript considers the problem of ensuring stability and safety during
formation control with distributed multi-agent systems in the presence of
parametric uncertainty in the dynamics and limited communication. We propose an
integrative approach that combines Control Barrier Functions, Adaptive Control,
and connected graphs. A reference model is designed so as to ensure a safe and
stable formation control strategy. This is combined with a provably correct
adaptive control design that includes a use of a CBF-based safety filter that
suitably generates safe reference commands, and employs error-based relaxation
(EBR) of Nagumo's Invariance Theorem. Together, it is shown to lead to a
guarantee of boundedness, formation control, and forward invariance. Numerical
examples are provided to support the theoretical derivations.
