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Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework

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2021

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Nastasi, Giovanni
Borzì, Alfio

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Journal of Computational and Theoretical Transport. Taylor & Francis. 2021, 50(5), pp. 454-482. ISSN 2332-4309. eISSN 2332-4325. Available under: doi: 10.1080/23324309.2021.1896552

Zusammenfassung

This paper is devoted to the formulation and numerical solution by Monte Carlo (MC) methods of an optimal control problem governed by the linear space-homogeneous Keilson-Storer (KS) master equation. The KS master equation is a representative model of the class of linear Boltzmann equations with many applications ranging from spectroscopy to transport theory. The purpose of the optimal control in the collision kernel of this model is to drive an ensemble of particles to acquire a desired mean velocity and to achieve a desired final velocity configuration. For this purpose, a KS optimality system characterizing the solution of the proposed optimal control problem is derived and used to construct a gradient-based optimization strategy in the framework of MC methods. This task requires to accommodate the resulting adjoint KS model in a form that is consistent with the kinetic formulation. Results of numerical experiments successfully validate the proposed control framework.

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Fachgebiet (DDC)
510 Mathematik

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Keilson-Storer master equation, linear Boltzmann equationen, semble optimal control, Monte Carlo methods

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ISO 690BARTSCH, Jan, Giovanni NASTASI, Alfio BORZÌ, 2021. Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework. In: Journal of Computational and Theoretical Transport. Taylor & Francis. 2021, 50(5), pp. 454-482. ISSN 2332-4309. eISSN 2332-4325. Available under: doi: 10.1080/23324309.2021.1896552
BibTex
@article{Bartsch2021Optim-58389,
  year={2021},
  doi={10.1080/23324309.2021.1896552},
  title={Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework},
  number={5},
  volume={50},
  issn={2332-4309},
  journal={Journal of Computational and Theoretical Transport},
  pages={454--482},
  author={Bartsch, Jan and Nastasi, Giovanni and Borzì, Alfio}
}
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