Title data
Fleig, Arthur ; Guglielmi, Roberto:
Optimal Control of the FokkerPlanck Equation with StateDependent Controls.
Bayreuth ; Linz
,
2016
.  21 S.
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2016_fleigguglielmi_optcontrolfpstatedependent.pdf  Preprint Available under License Deutsches Urheberrechtsgesetz . Download (296kB) 
Project information
Project title: 



Project financing: 
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 FokkerPlanck equation, a secondorder 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 FokkerPlanck 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 FokkerPlanck 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.
Further data
Item Type:  Preprint, postprint 

Keywords:  bilinear control; FokkerPlanck 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:703epub27945 
Date Deposited:  12 Apr 2016 07:46 
Last Modified:  12 Apr 2016 07:46 
URI:  https://epub.unibayreuth.de/id/eprint/2794 
Available Versions of this Item
 Optimal Control of the FokkerPlanck Equation with StateDependent Controls. (deposited 12 Apr 2016 07:46) [Currently Displayed]