Social optima in robust mean field LQG control

This paper studies mean field linear-quadratic-Gaussian (LQG) social optimum control for mean field models with a common uncertain drift, where both dynamics and costs of agents involve coupled terms. We adopt a robust optimization approach where all the agents view the uncertain drift as an adversarial player. Based on the social variational derivation and the person-by-person optimality principle, we construct an auxiliary optimal control problem for a representative agent. By solving the auxiliary problem combined with consistent mean field approximations, a set of decentralized strategies is designed and further shown to be asymptotically robust optimal.