The Distributionally Robust Infinite-Horizon LQR

Understand

We explore the infinite-horizon Distributionally Robust (DR) linear-quadratic control.

• While the probability distribution of disturbances is unknown and potentially correlated over time, it is confined within a Wasserstein-2 ball of a radius $r$ around a known nominal distribution.
• Our goal is to devise a control policy that minimizes the worst-case expected Linear-Quadratic Regulator (LQR) cost among all probability distributions of disturbances lying in the Wasserstein ambiguity set.
• We obtain the optimality conditions for the optimal DR controller and show that it is non-rational.