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

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.

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• Adjoint DSMC for Nonlinear Spatially-Homogeneous Boltzmann Equation With a General Collision Model