A new framework for the optimal control of probability density functions (PDF) of stochastic processes is reviewed. This framework is based on Fokker–Planck (FP) partial differential equations that govern the time evolution of the PDF of stochastic systems and on control objectives that may require to follow a given PDF trajectory or to minimize an expectation functional.
Classification :
34-XX, 35-XX, 49-XX, 65-XX
Mots-clés :
Fokker–Planck equations, Hamilton–Jacobi–Bellman equation, stochastic process, hybrid systems, Markov renewal processes, probability density function, mean-field approach, optimal control theory, model predictive control, numerical analysis, scientific computing
Affiliations des auteurs :
Mario Annunziato
1
;
Alfio Borzì
2
1
Università degli Studi di Salerno, Fisciano, Italy
2
Universität Würzburg, Germany
Mario Annunziato; Alfio Borzì. A Fokker–Planck control framework for stochastic systems. EMS surveys in mathematical sciences, Tome 5 (2018), pp. 65-98. doi: 10.4171/emss/27
@article{10_4171_emss_27,
author = {Mario Annunziato and Alfio Borz{\`\i}},
title = {A {Fokker{\textendash}Planck} control framework for stochastic systems},
journal = {EMS surveys in mathematical sciences},
pages = {65--98},
year = {2018},
volume = {5},
doi = {10.4171/emss/27},
url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/27/}
}
TY - JOUR
AU - Mario Annunziato
AU - Alfio Borzì
TI - A Fokker–Planck control framework for stochastic systems
JO - EMS surveys in mathematical sciences
PY - 2018
SP - 65
EP - 98
VL - 5
UR - http://geodesic.mathdoc.fr/articles/10.4171/emss/27/
DO - 10.4171/emss/27
ID - 10_4171_emss_27
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%T A Fokker–Planck control framework for stochastic systems
%J EMS surveys in mathematical sciences
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%P 65-98
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%U http://geodesic.mathdoc.fr/articles/10.4171/emss/27/
%R 10.4171/emss/27
%F 10_4171_emss_27
