Strict dissipativity analysis for classes of optimal control problems involving probability density functions

Title data

Fleig, Arthur ; Grüne, Lars:
Strict dissipativity analysis for classes of optimal control problems involving probability density functions.
In: Mathematical Control and Related Fields. (January 2021) . - pp. 1-30.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2020053

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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

Motivated by the stability and performance analysis of model predictive control schemes, we investigate strict dissipativity for a class of optimal control problems involving probability density functions. The dynamics are governed by a Fokker-Planck partial differential equation. However, for the particular classes under investigation involving linear dynamics, linear feedback laws, and Gaussian probability density functions, we are able to significantly simplify these dynamics. This enables us to perform an in-depth analysis of strict dissipativity for different cost functions.

Further data

Item Type:	Article in a journal
Refereed:	Yes
Keywords:	Model predictive control; Control theory; Optimal control; Partial differential equations; Stochastic processes; Fokker-planck equation; Dissipativity
Subject classification:	MSC 2020. Primary: 35Q84, 35Q93, 60G15; Secondary: 49N35, 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 Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Computer Science > Chair Applied Computer Science VIII 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) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Computer Science Profile Fields Profile Fields > Advanced Fields
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	12 Jan 2021 09:14
Last Modified:	12 Jan 2021 09:14
URI:	https://eref.uni-bayreuth.de/id/eprint/61653

Available Versions of this Item

Strict dissipativity analysis for classes of optimal control problems involving probability density functions. (deposited 13 Jul 2019 21:00)
- Strict dissipativity analysis for classes of optimal control problems involving probability density functions. (deposited 12 Jan 2021 09:14) [Currently Displayed]