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.

Keywords: 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}, zbl = {1269.93138}, mrnumber = {3092364}, 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 DA - 2013/// SP - 828 EP - 843 VL - 19 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012035/ UR - https://zbmath.org/?q=an%3A1269.93138 UR - https://www.ams.org/mathscinet-getitem?mr=3092364 UR - https://doi.org/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 https://doi.org/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, Volume 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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