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Estimates on the Minimal Stabilizing Horizon Length in Model Predictive Control for the Fokker-Planck Equation

URN to cite this document: urn:nbn:de:bvb:703-epub-2687-5

Title data

Fleig, Arthur ; Grüne, Lars:
Estimates on the Minimal Stabilizing Horizon Length in Model Predictive Control for the Fokker-Planck Equation.
Bayreuth , 2016 . - 6 S.

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2016_fleig-gruene_min-stab-horizon-mpc-fp.pdf - Preprint
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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 a series of papers by Annunziato and Borzì, Model Predictive Control of the Fokker-Planck equation has been established as a numerically feasible way for controlling stochastic processes via their probability density functions. Numerical simulations suggest that the resulting controller yields an asymptotically stable closed loop system for optimization horizons looking only one time step into the future. In this paper we provide a formal proof of this fact for the Fokker-Planck equation corresponding to the controlled Ornstein-Uhlenbeck process using an L² cost and control functions which are constant in space. The key step of the proof consists in the verification of an exponential controllability property with respect to the stage cost. Numerical simulations are provided to illustrate our results.

Further data

Item Type: Preprint, postprint
Keywords: model predictive control; optimal control; partial differential equations; stabilizing feedback; stochastic processes
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: 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 Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-2687-5
Date Deposited: 18 Jan 2016 10:47
Last Modified: 28 Mar 2019 14:52
URI: https://epub.uni-bayreuth.de/id/eprint/2687

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