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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 titleProject's id
Marie Curie Initial Training Network FP7-PEOPLE-2010-ITN SADCOGA 264735-SADCO
Model Predictive Control for the Fokker-Planck EquationGR 1569/15-1

Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union
Deutsche Forschungsgemeinschaft
Istituto Nazionale di Alta Matematica (INdAM)

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
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: 28 Mar 2019 10:25
URI: https://epub.uni-bayreuth.de/id/eprint/3361

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