  Pursuing a drifting target in a turbulent flow is an extremely difficult task
whenever the searcher has limited propulsion and maneuvering capabilities. Even
in the case when the relative distance between pursuer and target stays below
the turbulent dissipative scale, the chaotic nature of the trajectory of the
target represents a formidable challenge. Here, we show how to successfully
apply optimal control theory to find navigation strategies that overcome
chaotic dispersion and allow the searcher to reach the target in a minimal
time. We contrast the results of optimal control -- which requires perfect
observability and full knowledge of the dynamics of the environment -- with
heuristic algorithms that are reactive -- relying on local, instantaneous
information about the flow. While the latter display significantly worse
performances, optimally controlled pursuers can track the target for times much
longer than the typical inverse Lyapunov exponent and are considerably more
robust.
