This paper obtains a maximum principle for switching diffusions with mean-field interactions. The motivation stems from a wide range of applications for networked control systems in which large-scale systems are encountered and mean-field interactions are involved. Because of the complexity due to the switching, little has been done for the associate control problems with mean-field interactions. The main ingredient of this work is the use of conditional mean-fields, which is distinct from the existing literature. Using the maximum principle, optimal controls of linear quadratic Gaussian controls with mean-field interactions for switching diffusions are carried out. Numerical examples are also provided for demonstration.
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DOI : 10.1051/cocv/2019055
Mots-clés : Maximum principle, mean-field interaction, switching diffusion
@article{COCV_2020__26_1_A69_0,
author = {Nguyen, Son L. and Nguyen, Dung T. and Yin, George},
title = {A stochastic maximum principle for switching diffusions using conditional mean-fields with applications to control problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019055},
mrnumber = {4151428},
zbl = {1460.60082},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2019055/}
}
TY - JOUR AU - Nguyen, Son L. AU - Nguyen, Dung T. AU - Yin, George TI - A stochastic maximum principle for switching diffusions using conditional mean-fields with applications to control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2019055/ DO - 10.1051/cocv/2019055 LA - en ID - COCV_2020__26_1_A69_0 ER -
%0 Journal Article %A Nguyen, Son L. %A Nguyen, Dung T. %A Yin, George %T A stochastic maximum principle for switching diffusions using conditional mean-fields with applications to control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2019055/ %R 10.1051/cocv/2019055 %G en %F COCV_2020__26_1_A69_0
Nguyen, Son L.; Nguyen, Dung T.; Yin, George. A stochastic maximum principle for switching diffusions using conditional mean-fields with applications to control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 69. doi : 10.1051/cocv/2019055. http://archive.numdam.org/articles/10.1051/cocv/2019055/
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The research of S. Nguyen was supported by a seed fund of Department of Mathematics at University of Puerto Rico, Rio Piedras campus; the research of D. Nguyen was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2015.28; the research of G. Yin was supported in part by the Army Research Office under grant W911NF-19-1-0176.
