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Optimal Control of the Fokker-Planck Equation with Space-Dependent Controls

URN to cite this document: urn:nbn:de:bvb:703-epub-3361-2

Title data

Fleig, Arthur ; Guglielmi, Roberto:
Optimal Control of the Fokker-Planck Equation with Space-Dependent Controls.
Bayreuth ; Linz , 2017 . - 20 S.

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Project information

Project title:	Project's official title Project's id SADCO - Sensitivity Analysis for Deterministic Controller Design 264735 Modellprädiktive Regelung für die Fokker-Planck-Gleichung 264433583
Project financing:	7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union Deutsche Forschungsgemeinschaft Istituto Nazionale di Alta Matematica (INdAM) Marie-Curie Initial Training Network

Abstract

This paper is devoted to the analysis of a bilinear optimal control problem subject to the Fokker-Planck equation. The control function depends on time and space and acts as a coefficient of the advection term. For this reason, suitable integrability properties of the control function are required to ensure well-posedness of the state equation. Under these low regularity assumptions and for a general class of objective functionals, we prove the existence of optimal controls. Moreover, for common quadratic cost functionals of tracking and terminal type, we derive the system of first order necessary optimality conditions.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erschienen in: Journal of Optimization Theory and Applications. Bd. 174 (August 2017) Heft 2 . - S. 408-427. DOI: https://doi.org/10.1007/s10957-017-1120-5
Keywords:	bilinear control; Fokker-Planck equation; optimal control theory; optimization in Banach spaces; probability density function; stochastic process
Subject classification:	Mathematics Subject Classification (2010): 35Q84 35Q93 49J20 49K20
DDC Subjects:	500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields > Advanced Fields > Nonlinear Dynamics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Profile Fields Profile Fields > Advanced Fields
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-3361-2
Date Deposited:	09 Aug 2017 05:51
Last Modified:	16 Dec 2025 08:37
URI:	https://epub.uni-bayreuth.de/id/eprint/3361

Available Versions of this Item

Optimal Control of the Fokker-Planck Equation with State-Dependent Controls. (deposited 12 Apr 2016 07:46)
- Optimal Control of the Fokker-Planck Equation with Space-Dependent Controls. (deposited 02 Jun 2017 08:16)
  - Optimal Control of the Fokker-Planck Equation with Space-Dependent Controls. (deposited 09 Aug 2017 05:51) [Currently Displayed]