  We consider the problem of stochastic prediction and control in a
time-dependent stochastic environment, such as the ocean, where escape from an
almost invariant region occurs due to random fluctuations. We determine
high-probability control-actuation sets by computing regions of uncertainty,
almost invariant sets, and Lagrangian Coherent Structures. The combination of
geometric and probabilistic methods allows us to design regions of control that
provide an increase in loitering time while minimizing the amount of control
actuation. We show how the loitering time in almost invariant sets scales
exponentially with respect to the control actuation, causing an exponential
increase in loitering times with only small changes in actuation force. The
result is that the control actuation makes almost invariant sets more
invariant.
