Optimality of Linear Policies in Distributionally Robust Linear Quadratic Control

We generalize LQG control to a broad family of ambiguity sets around a nominal Gaussian distribution. The worst-case distribution is itself Gaussian, with zero mean and an inflated covariance, and the optimal controller remains linear in the observations. These structural results yield a Frank-Wolfe algorithm that outperforms semidefinite-programming reformulations and extend to infinite-horizon control; under Wasserstein ambiguity, they also hold for elliptical nominal distributions.

Major revision at Management Science