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A robust MPC for constrained discrete-time nonlinear system with additive uncertainties is presented. The MPC is based on the so called uncertain evolution sets, which are the sets containing the predicted evolution of the uncertain system under any admissible uncertainty. These sets are incorporated in the MPC formulation in order to achieve robust stability. By choosing as terminal constraint a robust positively invariant set, a dual-mode controller with guaranteed robust stability is obtained. Stability is guaranteed despite suboptimality of the computed solution. This controller is applied to a highly nonlinear system: a simulation model of a CSTR for an exothermic irreversible reaction. The uncertain evolution sets are computed on-line by using interval arithmetic. This procedure obtains quite good results with a similar computational effort than the nominal prediction.