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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 (15 September 2018) Issue 4 . - 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 titleProject's id
Model Predictive Control for the Fokker-Planck EquationGR 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 (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: 26 Sep 2019 07:13
URI: https://eref.uni-bayreuth.de/id/eprint/45895

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