Volume 26, 2020
|Number of page(s)||26|
|Published online||21 September 2020|
A stochastic maximum principle for switching diffusions using conditional mean-fields with applications to control problems*
Department of Mathematics, University of Puerto Rico, Rio Piedras campus,
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: firstname.lastname@example.org
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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