Robust linear quadratic mean field social control: A direct approach

Tinghan Xie, Bing Chang Wang, Jianhui Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper investigates a robust linear quadratic mean field team control problem. The model involves a global uncertainty drift which is common for a large number of weakly-coupled interactive agents. All agents treat the uncertainty as an adversarial agent to obtain a "worst case"disturbance. The direct approach is applied to solve the robust social control problem, where the state weight is allowed to be indefinite. Using variational analysis, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) and the centralized controls which contain the population state average. Then the decentralized feedback-type controls are designed by mean field heuristics. Finally, the relevant asymptotically social optimality is further proved under proper conditions.

Original languageEnglish
Article number2021021
Pages (from-to)1-19
Number of pages19
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume27
DOIs
Publication statusAccepted/In press - 12 Feb 2021

Keywords

  • Forward-backward stochastic differential equation
  • Linear quadratic control
  • Mean field game
  • Model uncertainty
  • Social optimality

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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