  Devising optimal interventions for constraining stochastic systems is a
challenging endeavour that has to confront the interplay between randomness and
nonlinearity. Existing methods for identifying the necessary dynamical
adjustments resort either to space discretising solutions of ensuing partial
differential equations, or to iterative stochastic path sampling schemes. Yet,
both approaches become computationally demanding for increasing system
dimension. Here, we propose a generally applicable and practically feasible
non-iterative methodology for obtaining optimal dynamical interventions for
diffusive nonlinear systems. We estimate the necessary controls from an
interacting particle approximation to the logarithmic gradient of two forward
probability flows evolved following deterministic particle dynamics. Applied to
several biologically inspired models, we show that our method provides the
necessary optimal controls in settings with terminal-, transient-, or
generalised collective-state constraints and arbitrary system dynamics.
