ERef Bayreuth

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

Title data

Fleig, Arthur ; Grüne, Lars:
L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation.
In: Vietnam Journal of Mathematics. Vol. 46 (2018) . - pp. 915-948.
ISSN 2305-2228
DOI: https://doi.org/10.1007/s10013-018-0309-8

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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 in another language

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:	Article in a journal
Refereed:	Yes
Keywords:	Model Predictive Control; Fokker-Planck equation; Probability density function; Stochastic optimal control
Subject classification:	Mathematics Subject Classification (2010): 35Q84 35Q93 49N35 60G15 93C15
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
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	15 Oct 2018 06:11
Last Modified:	06 Oct 2023 08:12
URI:	https://eref.uni-bayreuth.de/id/eprint/45895

Available Versions of this Item

L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation. (deposited 10 Feb 2018 22:00)
- L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation. (deposited 13 Feb 2018 08:38)
  - L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation. (deposited 15 Oct 2018 06:11) [Currently Displayed]