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On Dissipativity of the Fokker-Planck Equation for the Ornstein-Uhlenbeck Process

URN to cite this document: urn:nbn:de:bvb:703-epub-4084-8

Title data

Fleig, Arthur ; Grüne, Lars:
On Dissipativity of the Fokker-Planck Equation for the Ornstein-Uhlenbeck Process.
Bayreuth , 2018 . - 7 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

We study conditions for stability and near optimal behavior of the closed loop generated by Model Predictive Control for tracking Gaussian probability density functions associated with linear stochastic processes. More precisely, we analyze whether the corresponding optimal control problems are strictly dissipative. This is the key property required to infer statements about stability and performance of the closed loop system when tracking so-called unreachable setpoints, in which case a nonnegative cost is induced at the desired state. For verifying strict dissipativity, the choice of the so-called storage function is crucial. We focus on linear ones due to their close connection to the Lagrange function. The Ornstein-Uhlenbeck process serves as a prototype for our analysis, in which we show the limits of linear storage functions and present nonlinear alternatives, thus providing structural insight into dissipativity in case of bilinear system dynamics.

Further data

Item Type:	Preprint, postprint
Keywords:	Model Predictive Control; Stochastic Processes; Fokker-Planck Equation; Dissipativity; Probability Density Function; Ornstein-Uhlenbeck Process
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-4084-8
Date Deposited:	21 Dec 2018 08:05
Last Modified:	21 Dec 2018 08:05
URI:	https://epub.uni-bayreuth.de/id/eprint/4084

Available Versions of this Item

On Dissipativity of the Fokker-Planck Equation for the Ornstein-Uhlenbeck Process. (deposited 21 Dec 2018 08:05) [Currently Displayed]
- On Dissipativity of the Fokker-Planck Equation for the Ornstein-Uhlenbeck Process. (deposited 11 Mar 2019 15:20)

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