Robust Constrained Model Predictive Control using Closed-loop Prediction

This paper proposes a quadratic programming (QP) approach to robust MPC for constrained linear systems having both model uncertainties and bounded disturbances. To this end, we construct an additional comparison model for worst-case analysis based on a robust control Lyapunov function (RCLF) for the unconstrained system (not necessarily an RCLF in the presence of constraints). By using this comparison model, we transform the given robust MPC problem to a nominal one without uncertain terms. This comparison model also enables us to derive a terminal condition for ensuring the robust stability of the closed-loop. Since this terminal condition is described by linear constraints, the control optimization can be reduced to a QP problem.