Distributionally robust two-stage model predictive control: adaptive constraint tightening with stability guarantee

This paper proposes a two-stage distributionally robust model predictive control (TSDR-MPC) scheme for stochastic disturbances with unknown time-varying means and covariances. By defining a Wasserstein ambiguity set on the disturbance-to-constraint space, constraint violation penalties are formulated as a second-stage problem, enabling adaptive tightening. A finitely convergent cutting-plane algorithm is developed for real-time implementation. The framework naturally degrades to deterministic MPC as uncertainty vanishes, without pre-specified tightening parameters. Theoretical guarantees include feasibility, finite-time termination, and an asymptotic average cost bound. Numerical simulations validate its adaptability and robustness.