  To establish general principles of optimal control of active matter, we study
the elementary problem of moving an active particle by a trap with minimum work
input. We show analytically that (open-loop) optimal protocols are not affected
by activity, but work fluctuations are always increased. For closed-loop
protocols, which rely on initial measurements of the self-propulsion, the
average work has a minimum for a finite persistence time. Using these insights,
we derive an optimal cyclic active information engine, which is found to have a
higher precision and information efficiency when operated with a run-and-tumble
particle than for an active Ornstein-Uhlenbeck particle and, we argue, than for
any other type of active particle.
