Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-Disturbance
This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a representative agent in the limiting model views the drift uncertainty as an adversarial player. By including the mean field dynamics in an augmented state space, we solve two optimal control problems sequentially, which combined with consistent mean field approximations provides a solution to the robust game. A set of decentralized control strategies is derived by use of forward-backward stochastic differential equations (FBSDE) and shown to be a robust epsilon-Nash equilibrium.
- Pub Date:
- December 2016
- Mathematics - Optimization and Control;
- A preliminary version was presented at the 2015 IEEEE Conference on Decision and Control