Distributionally Robust System Level Synthesis With Output Feedback Affine Control Policy

This paper studies the finite-horizon robust optimal control of constrained linear systems subject to model mismatch and additive stochastic disturbances. Utilizing the system level synthesis (SLS) parameterization, we propose a novel SLS design using an output-feedback affine control policy and extend it to a distributionally robust setting to improve system resilience by minimizing the cost function while ensuring constraint satisfaction against the worst-case uncertainty distribution. The scopes of model mismatch and stochastic disturbances are quantified using the 1-norm and a Wasserstein metric-based ambiguity set, respectively. For the closed-loop dynamics, we analyze the distributional shift between the predicted output-input response -- computed using nominal parameters and empirical disturbance samples -- and the actual closed-loop distribution, highlighting its dependence on model mismatch and SLS parameterization. Assuming convex and Lipschitz continuous cost functions and constraints, we derive a tractable reformulation of the distributionally robust SLS (DR-SLS) problem by leveraging tools from robust control and distributionally robust optimization (DRO). Numerical experiments validate the performance and robustness of the proposed approach.