  A novel perspective on the design of robust model predictive control (MPC)
methods is presented, whereby closed-loop constraint satisfaction is ensured
using recursive feasibility of the MPC optimization. Necessary and sufficient
conditions are derived for recursive feasibility, based on the effects of model
perturbations and disturbances occurring at one time step. Using these
conditions and Farkas' lemma, sufficient conditions suitable for design are
formulated. The proposed method is called a closed-loop design, as only the
existence of feasible inputs at the next time step is enforced by design. This
is in contrast to most existing formulations, which compute control policies
that are feasible under the worst-case realizations of all model perturbations
and exogenous disturbances in the MPC prediction horizon. The proposed method
has an online computational complexity similar to nominal MPC methods while
preserving guarantees of constraint satisfaction, recursive feasibility and
stability. Numerical simulations demonstrate the efficacy of our proposed
approach.
