Weak Closed-loop Solvability of Linear Quadratic Stochastic Optimal Control Problems with Partial Information
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910619617198080 |
|---|---|
| author | Li, Xun Wang, Guangchen Xiong, Jie Zhang, Heng |
| author_facet | Li, Xun Wang, Guangchen Xiong, Jie Zhang, Heng |
| contents | This paper investigates a linear quadratic stochastic optimal control (LQSOC) problem with partial information. Firstly, by introducing two Riccati equations and a backward stochastic differential equation (BSDE), we solve this LQSOC problem under standard positive semidefinite assumptions. Secondly, by means of a perturbation approach, we study open-loop solvability of this problem when the weighting matrices in the cost functional are indefinite. Thirdly, we investigate weak closed-loop solvability of this problem and prove the equivalence between open-loop and weak closed-loop solvabilities. Finally, we give an example to illustrate the way for obtaining a weak closed-loop optimal strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak Closed-loop Solvability of Linear Quadratic Stochastic Optimal Control Problems with Partial Information Li, Xun Wang, Guangchen Xiong, Jie Zhang, Heng Optimization and Control This paper investigates a linear quadratic stochastic optimal control (LQSOC) problem with partial information. Firstly, by introducing two Riccati equations and a backward stochastic differential equation (BSDE), we solve this LQSOC problem under standard positive semidefinite assumptions. Secondly, by means of a perturbation approach, we study open-loop solvability of this problem when the weighting matrices in the cost functional are indefinite. Thirdly, we investigate weak closed-loop solvability of this problem and prove the equivalence between open-loop and weak closed-loop solvabilities. Finally, we give an example to illustrate the way for obtaining a weak closed-loop optimal strategy. |
| title | Weak Closed-loop Solvability of Linear Quadratic Stochastic Optimal Control Problems with Partial Information |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.16924 |