Robust Mean-Field LQ Optimal Control System with Partial Observation

Abstract

We investigate a robust mean-field linear-quadratic (MFLQ) control problem under partial observation. Two candidate models are evaluated through a worst-case criterion, while the state dynamics contain mean-field terms and the observation. We derive a sufficient optimality condition, a filtered state feedback representation, and two Riccati equations for the feedback gains. The reference probability is characterized through the continuity of the two model costs. Finally, deterministic Lyapunov equations provide a computable expression for the optimal cost and a numerical analysis for determining the robust reference probability.