H2/H∞ Stochastic Control Problem for Continuous-Time Mean-Field Stochastic Systems on Infinite Horizon

• 成果类型: Article
• 署名作者: Fang, Xuling; Li, Xun; Meng, Qingxin; Tang, Maoning
• 署名单位: Huzhou Normal University; Hong Kong Polytechnic University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3647805
• 发表日期: 2026
• 关键词: feedback; state

摘要

In this paper, we study the H-2/H-infinity control problem for continuous-time mean-field stochastic systems on an infinite horizon. Our primary objective is to establish a comprehensive framework that ensures both robust performance and optimal control for such systems. First, we derive an infinite-horizon mean-field stochastic bounded real lemma, demonstrating the equivalence between H-infinity robustness and the solution to two generalized algebraic Riccati equations. We then show that the existence of an H-2/H-infinity controller depends on the solvability of two sets of cross-coupled GAREs. In addition, we derive the optimal control input and the worst-case disturbance, which are formulated as linear state feedback laws incorporating both the system state and its mean. Furthermore, a numerical example is provided, demonstrating the solution of four intricately coupled matrix-valued equations.