Control of stochastic interacting particle systems is a non-trivial task due to the high dimensionality of the problem and the lack of fast algorithms. Here, we propose a space mapping-based approximation of the stochastic control problem by solutions of the deterministic one. In combination with the receding horizon control technique this yields a reliable and fast numerical scheme for the closed loop control of stochastic interacting particle systems. As a numerical example we consider the herding of sheep with dogs. The numerical results underline the feasibility of our approach and further show stabilizing behaviour of the closed loop control.

中文翻译：

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随机相互作用粒子系统的基于空间映射的后退地平线控制：放牧绵羊的狗

由于问题的高维性和缺乏快速算法，控制随机相互作用粒子系统是一项艰巨的任务。在此，我们通过确定性解决方案提出了一种基于空间映射的随机控制问题的近似方法。结合后退的水平控制技术，这为随机相互作用的粒子系统的闭环控制提供了可靠且快速的数值方案。作为一个数值示例，我们考虑用狗放牧绵羊。数值结果强调了我们方法的可行性，并进一步显示了闭环控制的稳定行为。