Space mapping-based Receding Horizon Control for Stochastic Interacting Particle Systems: dogs herding sheep

TL;DR

This paper introduces a space mapping-based approximation combined with receding horizon control to efficiently manage stochastic interacting particle systems, demonstrated through a sheep herding example.

Contribution

It presents a novel numerical scheme that approximates stochastic control problems via deterministic solutions, enabling fast and reliable control of high-dimensional systems.

Findings

The method effectively controls stochastic particle systems.

Numerical results show stable and feasible sheep herding control.

Approach reduces computational complexity of stochastic control.

Abstract

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.