A novel non-conservative robust nonlinear model predictive control scheme (NMPC) based on the multi-stage formulation is introduced for the case of an ellipsoidal uncertainty set. Multi-stage NMPC models uncertainty by a tree of discrete scenarios. In the case of a continuous-valued uncertainty, the scenario tree is usually built for all combinations of the minimum, nominal and maximum values of the uncertainty. If the uncertainty set is ellipsoidal, the standard multi-stage NMPC augments the uncertainty set which results in a performance loss while using the robust NMPC approaches. We propose to mitigate this problem by tightly over-approximating the uncertainty set using the so-called sigma points. An ellipsoidal over-approximation of the reachable set of the system is predicted along the prediction horizon using the unscented transformation. The advantages of the proposed scheme over the traditional multi-stage NMPC are demonstrated for a benchmark semi-batch reactor case study.
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