Extended recursively feasible Model Predictive Control by two-stage online optimization

In this work, a novel Model Predictive Control (MPC) scheme for the robust state-feedback stabilization of constrained discrete-time linear and nonlinear systems is proposed. In the last few years, invariant set theory has provided sufficient conditions to ensure the recursive feasibility of the constrained optimization problem associated to the MPC. In particular, it has emerged that the robustness of the classical MPC with stabilizing terminal state constraint depends on the invariance properties of the specified final constraint set. In this framework, with the aim to enlarge the set of admissible perturbations beyond the limit of one-step recursive feasibility, an algorithm based on two-stage optimization is presented. When only practical stabilization is needed, the devised method allows to use as terminal constraint also sets which are not one-step robustly controllable, while preserving the extended recursive feasibility property.