We study an extended mean-field control problem with partial observation, where the dynamic of the state is given by a forward-backward stochastic differential equation of McKean-Vlasov type. The cost functional, the state and the observation all depend on the joint distribution of the state and the control process. Our problem is motivated by the recent popular subject of mean-field games and related control problems of McKean-Vlasov type. We first establish a necessary condition in the form of Pontryagin’s maximum principle for optimality. Then a verification theorem is obtained for optimal control under some convex conditions of the Hamiltonian function. The results are also applied to studying linear-quadratic mean-filed control problem in the type of scalar interaction.
Keywords: Stochastic maximum principle, mean-field, forward-backward stochastic differential equation, partial observation
@article{COCV_2022__28_1_A17_0,
author = {Nie, Tianyang and Yan, Ke},
title = {Extended mean-field control problem with partial observation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2022010},
mrnumber = {4385098},
zbl = {1485.93638},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2022010/}
}
TY - JOUR AU - Nie, Tianyang AU - Yan, Ke TI - Extended mean-field control problem with partial observation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2022010/ DO - 10.1051/cocv/2022010 LA - en ID - COCV_2022__28_1_A17_0 ER -
%0 Journal Article %A Nie, Tianyang %A Yan, Ke %T Extended mean-field control problem with partial observation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2022010/ %R 10.1051/cocv/2022010 %G en %F COCV_2022__28_1_A17_0
Nie, Tianyang; Yan, Ke. Extended mean-field control problem with partial observation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 17. doi: 10.1051/cocv/2022010
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Cité par Sources :
This work is supported by the National Natural Science Foundation of China (Nos. 12022108, 11971267, 11831010, 61961160732, 61977043), Natural Science Foundation of Shandong Province (Nos. ZR2019ZD42, ZR2020ZD24), the Distinguished Young Scholars Program and Qilu Young Scholars Program of Shandong University.
