{"ID":2890093,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.19809","arxiv_id":"2507.19809","title":"\\(H_2/H_\\infty\\) Control for Continuous-Time Mean-Field Stochastic Systems with Affine Terms","abstract":"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.","short_abstract":"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} \\) nor...","url_abs":"https://arxiv.org/abs/2507.19809","url_pdf":"https://arxiv.org/pdf/2507.19809v1","authors":"[\"Xuling Fang\",\"Jun Moon\",\"Maoning Tang\",\"Qingxin Meng\"]","published":"2025-07-26T05:46:24Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}