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 language | English |
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Article number | 2021021 |
Pages (from-to) | 1-19 |
Number of pages | 19 |
Journal | ESAIM - Control, Optimisation and Calculus of Variations |
Volume | 27 |
DOIs | |
Publication status | Accepted/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