  This paper presents the formulation and analysis of a two time-scale
optimization algorithm for multi-agent coordination for the purpose of
distributed beamforming. Each agent is assumed to be randomly positioned with
respect to each other with random phase offsets and amplitudes. Agents are
tasked with coordinate among themselves to position themselves and adjust their
phase offset and amplitude such that they can construct a desired directed
beam. Here we propose a two time-scale optimization algorithm that consists of
a fast time-scale algorithm to solve for the amplitude and phase while a slow
time-scale algorithm to solve for the control required to re-position the
agents. The numerical results given here indicate that the proposed two
time-scale approach is able to reconstruct a desired beam pattern.
