Partially observed optimal controls of forward-backward doubly stochastic systems

Yufeng Shi; Qingfeng Zhu

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 3, page 828-843
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Shi, Yufeng, and Zhu, Qingfeng. "Partially observed optimal controls of forward-backward doubly stochastic systems." ESAIM: Control, Optimisation and Calculus of Variations 19.3 (2013): 828-843. <http://eudml.org/doc/272923>.

@article{Shi2013,
abstract = {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.},
author = {Shi, Yufeng, Zhu, Qingfeng},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {forward-backward doubly stochastic system; partially observed optimal control; maximum principle; adjoint equation; finite-dimensional spaces},
language = {eng},
number = {3},
pages = {828-843},
publisher = {EDP-Sciences},
title = {Partially observed optimal controls of forward-backward doubly stochastic systems},
url = {http://eudml.org/doc/272923},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 3
SP - 828
EP - 843
AB - 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.
LA - eng
KW - forward-backward doubly stochastic system; partially observed optimal control; maximum principle; adjoint equation; finite-dimensional spaces
UR - http://eudml.org/doc/272923
ER -

References

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