| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 69 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2019055 | |
| Published online | 21 September 2020 | |
A stochastic maximum principle for switching diffusions using conditional mean-fields with applications to control problems*
1
Department of Mathematics, University of Puerto Rico, Rio Piedras campus,
San Juan,
PR 00936, USA.
2
Department of Applied Mathematics, Faculty of Applied Science, University of Technology – Vietnam National University,
Ho Chi Minh city, Vietnam.
3
Department of Mathematics, Wayne State University,
Detroit,
MI 48202, USA.
** Corresponding author: gyin@wayne.edu
Received:
19
January
2019
Accepted:
1
September
2019
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.
Mathematics Subject Classification: 60J25 / 60J27 / 60J60 / 93E20
Key words: Maximum principle / mean-field interaction / switching diffusion
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.
© EDP Sciences, SMAI 2020
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