Weak Closed-loop Solvability for Discrete-time Stochastic Linear-Quadratic Optimal Control
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915167249367040 |
|---|---|
| author | Sun, Yue Wu, Xianping Li, Xun |
| author_facet | Sun, Yue Wu, Xianping Li, Xun |
| contents | In this paper, the solvability of discrete-time stochastic linear-quadratic (LQ) optimal control problem in finite horizon is considered. Firstly, it shows that the closed-loop solvability for the LQ control problem is optimal if and only if the generalized Riccati equation admits a regular solution by solving the forward and backward difference equations iteratively. To this ends, it finds that the open-loop solvability is strictly weaker than closed-loop solvability, that is, the LQ control problem is always open-loop optimal solvable if it is closed-loop optimal solvable but not vice versa. Secondly, by the perturbation method, it proves that the weak-closed loop strategy which is a feedback form of a state feedback representation is equivalent to the open-loop solvability of the LQ control problem. Finally, an example sheds light on the theoretical results established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak Closed-loop Solvability for Discrete-time Stochastic Linear-Quadratic Optimal Control Sun, Yue Wu, Xianping Li, Xun Optimization and Control org In this paper, the solvability of discrete-time stochastic linear-quadratic (LQ) optimal control problem in finite horizon is considered. Firstly, it shows that the closed-loop solvability for the LQ control problem is optimal if and only if the generalized Riccati equation admits a regular solution by solving the forward and backward difference equations iteratively. To this ends, it finds that the open-loop solvability is strictly weaker than closed-loop solvability, that is, the LQ control problem is always open-loop optimal solvable if it is closed-loop optimal solvable but not vice versa. Secondly, by the perturbation method, it proves that the weak-closed loop strategy which is a feedback form of a state feedback representation is equivalent to the open-loop solvability of the LQ control problem. Finally, an example sheds light on the theoretical results established. |
| title | Weak Closed-loop Solvability for Discrete-time Stochastic Linear-Quadratic Optimal Control |
| topic | Optimization and Control org |
| url | https://arxiv.org/abs/2502.16229 |