  A PDE-based control concept is developed to deploy a multi-agent system into
desired formation profiles. The dynamic model is based on a coupled linear,
time-variant parabolic distributed parameter system. By means of a particular
coupling structure parameter information can be distributed within the agent
continuum. Flatness-based motion planning and feedforward control are combined
with a backstepping-based boundary controller to stabilise the distributed
parameter system of the tracking error. The tracking controller utilises the
required state information from a Luenberger-type state observer. By means of
an exogenous system the relocation of formation profiles is achieved. The
transfer of the control strategy to a finite-dimensional discrete multi-agent
system is obtained by a suitable finite difference discretization of the
continuum model, which in addition imposes a leader-follower communication
topology. The results are evaluated both in simulation studies and in
experiments for a swarm of mobile robots realizing the transition between
different stable and unstable formation profiles.
