| Issue |
ESAIM: COCV
Volume 26, 2020
Special issue in honor of Enrique Zuazua's 60th birthday
|
|
|---|---|---|
| Article Number | 127 | |
| Number of page(s) | 28 | |
| DOI | https://doi.org/10.1051/cocv/2020081 | |
| Published online | 17 December 2020 | |
Stochastic linear quadratic optimal control problems for mean-field stochastic evolution equations*
School of Mathematics, Sichuan University,
Chengdu
610064,
Sichuan Province, PR China.
** Corresponding autjor: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
11
April
2020
Accepted:
18
November
2020
Abstract
We study a linear quadratic optimal control problem for mean-field stochastic evolution equation with the assumption that all the coefficients concerned in the problem are deterministic. We show that the existence of optimal feedback operators is equivalent to that of regular solution to the system which is coupled by two Riccati equations and an explicit formula of the optimal feedback control operator is given via the regular solution. We also show that the mentioned Riccati equations admit a unique strongly regular solution when the cost functional is uniformly convex.
Mathematics Subject Classification: 93E20 / 49N10 / 49N35
Key words: Mean-field stochastic evolution equation / linear quadratic optimal control problem / optimal feedback operator / Riccati equation
The research of this author is partially supported by NSF of China under grants 11971334, 11931011 and 12025105, and the Chang Jiang Scholars Program from the Chinese Education Ministry.
© EDP Sciences, SMAI 2020
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