The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied to study a partially-observed linear-quadratic optimal control problem for a fully coupled forward-backward doubly stochastic system.
Mots-clés : forward-backward doubly stochastic system, partially observed optimal control, maximum principle, adjoint equation
@article{COCV_2013__19_3_828_0,
author = {Shi, Yufeng and Zhu, Qingfeng},
title = {Partially observed optimal controls of forward-backward doubly stochastic systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {828--843},
publisher = {EDP-Sciences},
volume = {19},
number = {3},
year = {2013},
doi = {10.1051/cocv/2012035},
mrnumber = {3092364},
zbl = {1269.93138},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2012035/}
}
TY - JOUR AU - Shi, Yufeng AU - Zhu, Qingfeng TI - Partially observed optimal controls of forward-backward doubly stochastic systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 828 EP - 843 VL - 19 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012035/ DO - 10.1051/cocv/2012035 LA - en ID - COCV_2013__19_3_828_0 ER -
%0 Journal Article %A Shi, Yufeng %A Zhu, Qingfeng %T Partially observed optimal controls of forward-backward doubly stochastic systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 828-843 %V 19 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012035/ %R 10.1051/cocv/2012035 %G en %F COCV_2013__19_3_828_0
Shi, Yufeng; Zhu, Qingfeng. Partially observed optimal controls of forward-backward doubly stochastic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 828-843. doi : 10.1051/cocv/2012035. http://www.numdam.org/articles/10.1051/cocv/2012035/
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