\(H_2/H_\infty\) Control for Continuous-Time Mean-Field Stochastic Systems with Affine Terms
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_ | 1866915410944720896 |
|---|---|
| author | Fang, Xuling Moon, Jun Tang, Maoning Meng, Qingxin |
| author_facet | Fang, Xuling Moon, Jun Tang, Maoning Meng, Qingxin |
| contents | This paper discusses the \( H_2/H_{\infty} \) control problem for continuous-time mean-field linear stochastic systems with affine terms over a finite horizon. We employ the Mean-Field Stochastic Bounded Real Lemma (MF-SBRL), which provides the necessary and sufficient conditions to ensure that the \( H_{\infty} \) norm of system perturbations remains below a certain level. By utilizing the Mean-Field Forward-Backward Stochastic Differential Equations (MF-FBSDE), we establish the equivalence conditions for open-loop \( H_2/H_{\infty} \) control strategies. Furthermore, the paper demonstrates that the control problem is solvable under closed-loop conditions if solutions exist for four coupled Difference Riccati Equations (CDREs), two sets of backward stochastic differential equations (BSDEs) and ordinary equations (ODEs). The state-feedback gains for the control strategy can be derived from these solutions, thereby linking the feasibility of open-loop and closed-loop solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | \(H_2/H_\infty\) Control for Continuous-Time Mean-Field Stochastic Systems with Affine Terms Fang, Xuling Moon, Jun Tang, Maoning Meng, Qingxin Optimization and Control This paper discusses the \( H_2/H_{\infty} \) control problem for continuous-time mean-field linear stochastic systems with affine terms over a finite horizon. We employ the Mean-Field Stochastic Bounded Real Lemma (MF-SBRL), which provides the necessary and sufficient conditions to ensure that the \( H_{\infty} \) norm of system perturbations remains below a certain level. By utilizing the Mean-Field Forward-Backward Stochastic Differential Equations (MF-FBSDE), we establish the equivalence conditions for open-loop \( H_2/H_{\infty} \) control strategies. Furthermore, the paper demonstrates that the control problem is solvable under closed-loop conditions if solutions exist for four coupled Difference Riccati Equations (CDREs), two sets of backward stochastic differential equations (BSDEs) and ordinary equations (ODEs). The state-feedback gains for the control strategy can be derived from these solutions, thereby linking the feasibility of open-loop and closed-loop solutions. |
| title | \(H_2/H_\infty\) Control for Continuous-Time Mean-Field Stochastic Systems with Affine Terms |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.19809 |