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.

翻译：设计限制随机和非线性系统的最佳干预措施是一项挑战性的工作,必须应对随机性和非线性之间的相互作用。现有的确定必要动态调整的方法,要么采用空间分解的局部差异方程式解决方案,要么采用迭接的随机路径抽样办法。然而,这两种办法在计算上都要求增加系统的维度。在这里,我们提出了一个普遍适用和切实可行、非线性系统获得最佳动态干预措施的非线性方法。我们估计了在确定性粒子动态之后,两种前方概率流的对数梯度的交互粒子近似所需的控制。我们应用了几个生物启发模型,显示我们的方法在终端、瞬变或一般集体状态制约和任意系统动态的环境中提供了必要的最佳控制。