L2-Tracking of Gaussian Distributions via Model Predictive Control for the Fokker–Planck Equation

This paper presents the 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 referen...

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Bibliographic Details
Published inVietnam journal of mathematics Vol. 46; no. 4; pp. 915 - 948
Main Authors Fleig, Arthur, Grüne, Lars
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.12.2018
Subjects
Mathematics
Mathematics and Statistics
Fokker–Planck equation
Stochastic optimal control
93C15
Probability density function
35Q84
49N35
Model Predictive Control
35Q93
60G15
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Summary:This paper presents the 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 L 2 -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.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-018-0309-8