  We present a model for controlling swarms of mobile agents via broadcast
control, assumed to be detected by a random set of agents in the swarm. The
agents that detect the control signal become ad-hoc leaders of the swarm. The
agents are assumed to be velocity controlled, identical, anonymous, memory-less
units with limited capabilities of sensing their neighborhood. Each agent is
programmed to behave according to a linear local gathering process, based on
the relative position of all its neighbors. The detected exogenous control,
which is a desired velocity vector, is added by the leaders to the local
gathering control. The graph induced by the agents adjacency is referred to as
the visibility graph. We show that for piece-wise constant system parameters
and a connected visibility graph, the swarm asymptotically aligns in each
time-interval on a line in the direction of the exogenous control signal, and
all the agents move with identical speed. These results hold for two models of
pairwise influence in the gathering process, uniform and scaled. The impact of
the influence model is mostly evident when the visibility graph is incomplete.
These results are conditioned by the preservation of the connectedness of the
visibility graph. In the second part of the report we analyze sufficient
conditions for preserving the connectedness of the visibility graph. We show
that if the visibility graph is complete then certain bounds on the control
signal suffice to preserve the completeness of the graph. However, when the
graph is incomplete, general conditions, independent of the leaders topology,
could not be found.
