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

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 common for all agents. A robust optimization approach applied assuming agents treat drift as adversarial player. In our model, both dynamics and costs are coupled terms, finite- infinite-time horizon cases considered. By examining functional variation exploiting person-by-person optimality principle, we construct auxiliary problem generic agent via a class forward-backward stochastic differential equation system. solving constructing consistent approximation, set decentralized strategies designed shown to be asymptotically optimal.