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

URN zum Zitieren dieses Dokuments: urn:nbn:de:bvb:703-epub-2794-5

Titelangaben

Fleig, Arthur ; Guglielmi, Roberto:
Optimal Control of the Fokker-Planck Equation with State-Dependent Controls.
Bayreuth ; Linz , 2016 . - 21 S.

Volltext

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2016_fleig-guglielmi_opt-control-fp-state-dependent.pdf - Preprint
Available under License Deutsches Urheberrechtsgesetz .

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Angaben zu Projekten

Projekttitel:
Offizieller ProjekttitelProjekt-ID
Marie Curie Initial Training Network FP7-PEOPLE-2010-ITN SADCOGA 264735-SADCO
Model Predictive Control for the Fokker-Planck EquationGR 1569/15-1

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

Abstract

For a large class of stochastic processes, the evolution of the underlying probability density function is prescribed by a forward Kolmogorov equation, also called Fokker-Planck equation, a second-order parabolic partial differential equation. In this manner, an optimal control problem subject to an Itô stochastic differential equation can be rendered deterministic by recasting it as an optimal control problem for the Fokker-Planck equation, which we study in this work. In this setting, the control acts as a coefficient of the state variable in the advection term, i.e., it is of bilinear type. This optimal control problem has been firstly studied by Annunziato and Borzì (2010, 2013) for constant or time dependent controls. We extend the analysis to the case of time and space dependent controls, which allows to consider a wider variety of possible objectives. In order to deduce existence of nonnegative solutions for the state equation we require suitable integrability assumptions on the coefficients of the Fokker-Planck equation and thus on the control function. Therefore, the optimization takes place in a Banach space. We develop a systematic analysis of the existence of optimal controls and derive the system of first order necessary optimality conditions.

Weitere Angaben

Publikationsform: Preprint, Postprint, Working paper, Diskussionspapier
Keywords: bilinear control; Fokker-Planck equation; optimal control
theory; optimization in Banach spaces; probability density function; stochastic
process
Fachklassifikationen: Mathematics Subject Classification (2010): 35Q84 35Q93 49J20 49K20
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Profilfelder > Advanced Fields > Nichtlineare Dynamik
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Profilfelder
Profilfelder > Advanced Fields
Sprache: Englisch
Titel an der UBT entstanden: Ja
URN: urn:nbn:de:bvb:703-epub-2794-5
Eingestellt am: 12 Apr 2016 07:46
Letzte Änderung: 12 Apr 2016 07:46
URI: https://epub.uni-bayreuth.de/id/eprint/2794