  We establish a collection of closed-loop guarantees and propose a scalable,
Newton-type optimization algorithm for distributionally robust model predictive
control (DRMPC) applied to linear systems, zero-mean disturbances, convex
constraints, and quadratic costs. Via standard assumptions for the terminal
cost and constraint, we establish distribtionally robust long-term and
stage-wise performance guarantees for the closed-loop system. We further
demonstrate that a common choice of the terminal cost, i.e., as the solution to
the discrete-algebraic Riccati equation, renders the origin input-to-state
stable for the closed-loop system. This choice of the terminal cost also
ensures that the exact long-term performance of the closed-loop system is
independent of the choice of ambiguity set the for DRMPC formulation. Thus, we
establish conditions under which DRMPC does not provide a long-term performance
benefit relative to stochastic MPC (SMPC). To solve the proposed DRMPC
optimization problem, we propose a Newton-type algorithm that empirically
achieves superlinear convergence by solving a quadratic program at each
iteration and guarantees the feasibility of each iterate. We demonstrate the
implications of the closed-loop guarantees and the scalability of the proposed
algorithm via two examples.
