Robust model predictive control with disturbance invariant sets

This paper proposes a robust model predictive control scheme for nonlinear systems with state and input constraints and unknown but bounded disturbances. A standard nominal model predictive control problem with tightened constraints is solved online, and its solution defines the nominal trajectory. An ancillary control law is determined off-line which keeps the trajectories of the error system in a disturbance invariant set. Thus, the evolution of original nonlinear system lies in the disturbance invariant set centered along the nominal trajectory. Furthermore, it is shown that both feasibility and stability of the closed-loop system are guaranteed if the standard nominal optimization problem is initially feasible.