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

Bing Chang Wang, Jianhui Huang, Ji Feng Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number9097879
Pages (from-to)1529-1544
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number4
Publication statusPublished - Apr 2021


  • Forward-backward stochastic differential equation (FBSDE)
  • linear quadratic optimal control
  • mean field control
  • model uncertainty
  • social functional variation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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