A numerical investigation of Brockett’s ensemble optimal control problems
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- 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 andThis 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.…
Autor(en): | Jan Bartsch, Alfio Borzì, Francesco Fanelli, Souvik Roy |
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URN: | urn:nbn:de:bvb:20-opus-265352 |
Dokumentart: | Artikel / Aufsatz in einer Zeitschrift |
Institute der Universität: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Sprache der Veröffentlichung: | Englisch |
Titel des übergeordneten Werkes / der Zeitschrift (Englisch): | Numerische Mathematik |
Erscheinungsjahr: | 2021 |
Band / Jahrgang: | 149 |
Heft / Ausgabe: | 1 |
Seitenangabe: | 1–42 |
Originalveröffentlichung / Quelle: | Numerische Mathematik 2021, 149(1):1–42. DOI: 10.1007/s00211-021-01223-6 |
DOI: | https://doi.org/10.1007/s00211-021-01223-6 |
Allgemeine fachliche Zuordnung (DDC-Klassifikation): | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Freie Schlagwort(e): | Brockett; ensemble optimal control problems; numerical analysis |
Datum der Freischaltung: | 13.04.2022 |
Lizenz (Deutsch): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |