  Understanding the complex patterns in space-time exhibited by active systems
has been the subject of much interest in recent times. Complementing this
forward problem is the inverse problem of controlling active matter. Here we
use optimal control theory to pose the problem of transporting a slender drop
of an active fluid and determine the dynamical profile of the active stresses
to move it with minimal viscous dissipation. By parametrizing the position and
size of the drop using a low-order description based on lubrication theory, we
uncover a natural ''gather-move-spread'' strategy that leads to an optimal
bound on the maximum achievable displacement of the drop relative to its size.
In the continuum setting, the competition between passive surface tension, and
active controls generates richer behaviour with futile oscillations and complex
drop morphologies that trade internal dissipation against the transport cost to
select optimal strategies. Our work combines active hydrodynamics and optimal
control in a tractable and interpretable framework, and begins to pave the way
for the spatiotemporal manipulation of active matter.
