Optimal Distributionally Robust Control for Linear Quadratic Gaussian Systems under Distributed Uncertainty

The paper proposes a new paradigm for the robustification of the LQG controller against distributional uncertainties on the noise process. The controller optimizes the closed-loop performance in the worst possible scenario under the constraint that the noise distributional aberrance does not exceed a certain threshold limiting the relative entropy between the actual noise distribution and the nominal one. The key novelty is that the bounds on the distributional aberrance can be arbitrarily distributed along the whole disturbance trajectory.