On the stabilization of a kinetic model by feedback-like control fields in a Monte Carlo framework

TL;DR

This paper develops a feedback-like control strategy for a kinetic phase space model, using a Monte Carlo approach to stabilize particle densities along desired cyclic trajectories, demonstrated through numerical experiments.

Contribution

It introduces a novel ensemble optimal control formulation for kinetic models that is compatible with Monte Carlo methods, enabling stable trajectory tracking.

Findings

Control strategy effectively stabilizes particle densities

Numerical experiments confirm the approach's effectiveness

Method provides a one-shot solution via an augmented adjoint model

Abstract

The construction of feedback-like control fields for a kinetic model in phase space is investigated. The purpose of these controls is to drive an initial density of particles in the phase space to reach a desired cyclic trajectory and follow it in a stable way. For this purpose, an ensemble optimal control problem governed by the kinetic model is formulated in a way that is amenable to a Monte Carlo approach. The proposed formulation allows to define a one-shot solution procedure consisting in a backward solve of an augmented adjoint kinetic model. Results of numerical experiments demonstrate the effectiveness of the proposed control strategy.