Robust Mean Field Social Control Problems with Applications in Analysis of Opinion Dynamics

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This paper investigates the social optimality of linear quadratic mean field control systems with unmodeled dynamics.

• The objective of agents is to optimize the social cost, which is the sum of costs of all agents.
• By variational analysis and direct decoupling methods, the social optimal control problem is analyzed, and two equivalent auxiliary robust optimal control problems are obtained for a representative agent.
• By solving the auxiliary problem with consistent mean field approximations, a set of decentralized strategies is designed, and its asymptotic social optimality is further proved.