Recursive feasibility for DR-MPC with Wasserstein chance constraints

Establish recursive feasibility for the distributionally robust model predictive control formulation that enforces worst-case chance constraints over a Wasserstein ambiguity set around the nominal lifted system–environment distribution, by constructing appropriate terminal ingredients such as a distributionally robust terminal set and a terminal controller so that feasibility is maintained at all receding-horizon steps.

Background

The paper shows that feasibility of the DR-MPC problem at a given planning step, together with the L1-adaptive certificate and a finite-sample environment bound, implies stagewise safety. However, the authors explicitly note that these guarantees are not recursive, i.e., they do not ensure the MPC problem remains feasible at subsequent steps.

The authors state that achieving recursive feasibility would require terminal ingredients tailored to the distributionally robust setting (e.g., a distributionally robust terminal set and terminal controller). Formalizing and proving such recursive feasibility results would strengthen closed-loop guarantees for the proposed architecture.

References

\Cref{thm:closed_loop_safety} guarantees constraint satisfaction at each step for which~eqn:dr_mpc is feasible, but does not ensure recursive feasibility. If the DR-MPC problem becomes infeasible at some $t_k$, the guarantee no longer applies. Establishing recursive feasibility would require additional terminal ingredients, such as a distributionally robust terminal set and terminal controller, which we leave for future work.

— $\mathcal{L}_1$-Certified Distributionally Robust Planning for Safety-Constrained Adaptive Control  (2603.28758 - Hakobyan et al., 30 Mar 2026) in Footnote following Theorem “Closed-Loop Safety” (Theorem thm:closed_loop_safety), Section 3.3 “Distributional Certificates and Closed-Loop Safety”