Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizon

• 成果类型: Article
• 署名作者: Wang, Bing-Chang; Huang, Jianhui; Zhang, Ji-Feng
• 署名单位: Shandong University; Hong Kong Polytechnic University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2996189
• 发表日期: 2021
• 页码: 1529-1544
• 关键词: Mathematical model; games; Robustness; uncertainty; optimal control; Stochastic processes; Differential equations; Forward-backward stochastic differential equation (FBSDE); linear quadratic optimal control; mean field control; model uncertainty; social functional variation

摘要

This article studies social optimal control of mean field linear-quadratic-Gaussian models with uncertainty. Specially, the uncertainty is represented by an uncertain drift, which is common for all agents. A robust optimization approach is applied by assuming all agents treat the uncertain drift as an adversarial player. In our model, both dynamics and costs of agents are coupled by mean field terms, and both finite- and infinite-time horizon cases are considered. By examining social functional variation and exploiting person-by-person optimality principle, we construct an auxiliary control problem for the generic agent via a class of forward-backward stochastic differential equation system. By solving the auxiliary problem and constructing consistent mean field approximation, a set of decentralized control strategies is designed and shown to be asymptotically optimal.