A numerical investigation of Brockett’s ensemble optimal control problems

Bartsch, Jan; Borzì, Alfio; Fanelli, Francesco; Roy, Souvik

A numerical investigation of Brockett’s ensemble optimal control problems

Dateien

Bartsch_2-j1o4hh0j0m9z8.pdfGröße: 953.43 KBDownloads: 56

Datum

2021

Autor:innen

Bartsch, Jan

Borzì, Alfio

Fanelli, Francesco

Roy, Souvik

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Numerische Mathematik. Springer. 2021, 149(1), pp. 1-42. ISSN 0029-599X. eISSN 0945-3245. Available under: doi: 10.1007/s00211-021-01223-6

Zusammenfassung

This paper is devoted to the numerical analysis of non-smooth ensemble optimal control problems governed by the Liouville (continuity) equation that have been originally proposed by R.W. Brockett with the purpose of determining an efficient and robust control strategy for dynamical systems. A numerical methodology for solving these problems is presented that is based on a non-smooth Lagrange optimization framework where the optimal controls are characterized as solutions to the related optimality systems. For this purpose, approximation and solution schemes are developed and analysed. Specifically, for the approximation of the Liouville model and its optimization adjoint, a combination of a Kurganov–Tadmor method, a Runge–Kutta scheme, and a Strang splitting method are discussed. The resulting optimality system is solved by a projected semi-smooth Krylov–Newton method. Results of numerical experiments are presented that successfully validate the proposed framework.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

BARTSCH, Jan, Alfio BORZÌ, Francesco FANELLI, Souvik ROY, 2021. A numerical investigation of Brockett’s ensemble optimal control problems. In: Numerische Mathematik. Springer. 2021, 149(1), pp. 1-42. ISSN 0029-599X. eISSN 0945-3245. Available under: doi: 10.1007/s00211-021-01223-6

BibTex

@article{Bartsch2021numer-58557,
  year={2021},
  doi={10.1007/s00211-021-01223-6},
  title={A numerical investigation of Brockett’s ensemble optimal control problems},
  number={1},
  volume={149},
  issn={0029-599X},
  journal={Numerische Mathematik},
  pages={1--42},
  author={Bartsch, Jan and Borzì, Alfio and Fanelli, Francesco and Roy, Souvik}
}

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