Optimal Control of Stochastic Partial Differential Equations with Partial Observations: Stochastic Maximum Principles and Numerical Approximation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915251467845632 |
|---|---|
| author | Cao, Yanzhao Qian, Hongjiang Yin, George |
| author_facet | Cao, Yanzhao Qian, Hongjiang Yin, George |
| contents | This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a cylindrical Wiener process and finitely many Brownian motions, while observations are in an Euclidean space having correlated noise. For convex control domain and diffusion coefficients in the state being control-independent, numerical algorithms are developed to solve the partially observed optimal control problems using stochastic gradient descent algorithm combined with finite element approximations and the branching filtering algorithm. Numerical experiments are conducted for demonstration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Control of Stochastic Partial Differential Equations with Partial Observations: Stochastic Maximum Principles and Numerical Approximation Cao, Yanzhao Qian, Hongjiang Yin, George Optimization and Control 93E11, 60G35, 65K10, 60H15, 60H10 This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a cylindrical Wiener process and finitely many Brownian motions, while observations are in an Euclidean space having correlated noise. For convex control domain and diffusion coefficients in the state being control-independent, numerical algorithms are developed to solve the partially observed optimal control problems using stochastic gradient descent algorithm combined with finite element approximations and the branching filtering algorithm. Numerical experiments are conducted for demonstration. |
| title | Optimal Control of Stochastic Partial Differential Equations with Partial Observations: Stochastic Maximum Principles and Numerical Approximation |
| topic | Optimization and Control 93E11, 60G35, 65K10, 60H15, 60H10 |
| url | https://arxiv.org/abs/2504.14431 |