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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.

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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

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

L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation. (deposited 05 Feb 2018 06:29)
- L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation. (deposited 12 Feb 2018 08:04)
  - L²-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker-Planck Equation. (deposited 26 Sep 2019 07:11) [Currently Displayed]

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