| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 17 | |
| Number of page(s) | 43 | |
| DOI | https://doi.org/10.1051/cocv/2022010 | |
| Published online | 24 February 2022 | |
Extended mean-field control problem with partial observation*
School of Mathematics, Shandong University,
Jinan
250100, China.
** Corresponding author. 201812092@mail.sdu.edu.cn
Received:
4
March
2021
Accepted:
29
January
2022
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.
Mathematics Subject Classification: 93E20 / 60H10 / 60H30 / 60K35
Key words: Stochastic maximum principle / mean-field / forward-backward stochastic differential equation / partial observation
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.
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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