Wasserstein Distributionally Robust MPC for Cost-Weight Uncertainty Under Limited Data

Abstract

This paper considers a model predictive control (MPC) problem for discrete-time linear systems with uncertain cost-weight parameters under limited data. A Wasserstein ambiguity set centered at the empirical distribution is introduced, and a distributionally robust optimization-based MPC (DRO-MPC) framework is developed. The uncertainty is assumed to affect only the objective function, while the system dynamics and input constraints remain deterministic. It is shown that the DRO optimal value provides a finite-sample high-confidence upper certificate of the true out-of-sample finite-horizon predicted cost and converges asymptotically to the optimal value of the true stochastic MPC problem as the sample size increases. Recursive feasibility and nominal asymptotic stability are also established over the feasible set. Numerical results show that the proposed DRO-MPC method yields a more reliable finitesample certificate than sample average approximation-based MPC (SAA-MPC) in the small-sample regime.