Publications by the same author
plus in the repository
plus in Google Scholar

Bibliografische Daten exportieren
 

L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation

URN to cite this document: urn:nbn:de:bvb:703-epub-3862-3

Title data

Fleig, Arthur ; Grüne, Lars:
L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation.
Bayreuth , 2018 . - 33 S.

This is the latest version of this item.

Project information

Project title:
Project's official title
Project's id
Model Predictive Control for the Fokker-Planck Equation
GR 1569/15-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract

This paper presents first results for the stability analysis of Model Predictive Control schemes applied to the Fokker-Planck equation for tracking probability density functions. The analysis is carried out for linear dynamics and Gaussian distributions, where the distance to the desired reference is measured in the L²-norm. We present results for general such systems with and without control penalization. Refined results are given for the special case of the Ornstein-Uhlenbeck process. Some of the results establish stability for the shortest possible (discrete time) optimization horizon N=2.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen in:
Vietnam Journal of Mathematics. Bd. 46 (15 September 2018) Heft 4 . - S. 915-948.
DOI: https://doi.org/10.1007/s10013-018-0309-8
Keywords: Model Predictive Control; Fokker-Planck equation; Probability density function; Stochastic optimal control
Subject classification: Mathematics Subject Classification (2010): 35Q84 35Q93 49N35 60G15 93C15
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) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair 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
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3862-3
Date Deposited: 26 Sep 2019 07:11
Last Modified: 12 May 2021 10:31
URI: https://epub.uni-bayreuth.de/id/eprint/3862

Available Versions of this Item

Downloads

Downloads per month over past year