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.
Keywords: Backward stochastic differential equation, mean-field stochastic differential equation, exact controllability, controllability Gramian, Kalman rank condition
@article{COCV_2021__27_1_A32_0,
author = {Yu, Zhiyong},
title = {Controllability {Gramian} and {Kalman} rank condition for mean-field control systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021031},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021031/}
}
TY - JOUR AU - Yu, Zhiyong TI - Controllability Gramian and Kalman rank condition for mean-field control systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021031/ DO - 10.1051/cocv/2021031 LA - en ID - COCV_2021__27_1_A32_0 ER -
%0 Journal Article %A Yu, Zhiyong %T Controllability Gramian and Kalman rank condition for mean-field control systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021031/ %R 10.1051/cocv/2021031 %G en %F COCV_2021__27_1_A32_0
Yu, Zhiyong. Controllability Gramian and Kalman rank condition for mean-field control systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 30. doi: 10.1051/cocv/2021031
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