2024/05/28 by Francesco Micheli, Micheli, Francesco, Anastasios Tsiamis +3 · 1 citation
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2405.18142
openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a novel approach for the control of uncertain, linear time-invariant systems, which are perturbed by potentially unbounded, additive disturbances. We propose a doubly robust data-driven state-feedback controller to ensure reliable performance against both model mismatch and disturbance distribution uncertainty. Our controller, which leverages the System Level Synthesis parameterization, is designed as the solution to a distributionally robust finite-horizon optimal control problem. The goal is to minimize a cost function while satisfying constraints against the worst-case realization of the uncertainty, which is quantified using distributional ambiguity sets. The latter are defined as balls in the Wasserstein metric centered on the predictive empirical distribution computed from a set of collected trajectory data. By harnessing techniques from robust control and distributionally robust optimization, we characterize the distributional shift between the predictive and the actual closed-loop distributions, and highlight its dependency on the model mismatch and the uncertainty about the disturbance distribution. We also provide bounds on the number of samples required to achieve a desired confidence level and propose a tractable approximate formulation for the doubly robust data-driven controller. To demonstrate the effectiveness of our approach, we present a numerical example showcasing the performance of the proposed algorithm.