Once Upon a Time Step: A Closed-Loop Approach to Robust MPC Design

A novel robust model predictive control (MPC) algorithm is presented, whereby closed-loop constraint satisfaction is ensured using recursive feasibility of the MPC optimization. The proposed strategy considers the effects of model perturbations and disturbances occurring at only <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">one time step</i>. This is in contrast to 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 guaranteeing constraint satisfaction, recursive feasibility, and stability. Numerical simulations demonstrate the efficacy of our proposed approach.