| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 30 | |
| Number of page(s) | 28 | |
| DOI | https://doi.org/10.1051/cocv/2021031 | |
| Published online | 07 April 2021 | |
Controllability Gramian and Kalman rank condition for mean-field control systems
School of Mathematics, Shandong University,
Jinan
250100, PR China.
** Corresponding author: yuzhiyong@sdu.edu.cn
Received:
4
October
2020
Accepted:
15
March
2021
This paper is concerned with the exact controllability of linear mean-field stochastic systems with deterministic coefficients. With the help of the theory of mean-field backward stochastic differential equations (MF-BSDEs, for short) and some delicate analysis, we obtain a mean-field version of the Gramian matrix criterion for the general time-variant case, and a mean-field version of the Kalman rank condition for the special time-invariant case.
Mathematics Subject Classification: 60H10 / 93B05
Key words: Backward stochastic differential equation / mean-field stochastic differential equation / exact controllability / controllability Gramian / Kalman rank condition
© EDP Sciences, SMAI 2021
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