Urkmez and Heshmati-Alamdari's New Framework Masters Unknown Disturbances

The paper introduces a distributionally robust data‑driven predictive control (DR‑DD‑PC) framework for stochastic linear time‑invariant (LTI) systems where both the system dynamics and the disturbance distribution are unknown. The authors use an offline trajectory to fit a subspace predictive control (SPC) predictor via least squares. From this, they construct an empirical distribution of the prediction residuals, which serves as a proxy for the true disturbance distribution. A Wasserstein ambiguity set is centered around this empirical distribution, and the controller minimizes the worst‑case expected cost while enforcing probabilistic output constraints over all distributions within that set. The resulting optimization problem admits a tractable reformulation that directly uses the data, eliminating the need for explicit system identification.

The key technical contribution is the derivation of a data‑driven Wasserstein radius based on finite‑sample concentration inequalities. This radius ensures that, with high probability, the true expected cost is bounded by the tractable objective and that output constraints are satisfied under the true disturbance distribution. Numerical simulations compare the proposed method against existing approaches (e.g., robust MPC, scenario‑based MPC) under various disturbance conditions and cost functions. The results demonstrate improved performance and constraint satisfaction, especially when the disturbance distribution deviates from nominal assumptions. This work bridges data‑driven control and distributionally robust optimization, offering a principled way to handle uncertainty in real‑world control applications.