Scenario-based Model Predictive Control: Recursive Feasibility and Stability

Many processes are influenced by uncertain parameters or external disturbances, such as temperature changes. The control of such systems is in general challenging. In this work, we consider robust multi-scenario Model Predictive Control (MPC). Its central idea is to assume a finite number of possible values for the uncertainties and to model their combinations in a scenario tree. We adapt the classical dual mode approach of nominal MPC to establish recursive feasibility and stability for the multi-scenario case, using a common terminal region and common terminal cost function for all uncertainty realizations. For linear systems, the computation of these ingredients can be formulated as a semidefinite program. In a simulation, we apply the suggested approach to building climate control and show that it robustly stabilizes the system while a standard MPC controller violates state constraints and becomes infeasible.