Dual control is a technique that addresses the trade-off between probing (excitation signals) and control actions, which results in a better estimation of the unknown parameters and therefore in a better (tracking or economic) performance. Multi-stage NMPC is a robust-control scheme that represents the uncertainty using a scenario tree that is often built by assuming parametric uncertainty and by taking into account the minimum, nominal and maximum values of the uncertain parameters. If the uncertainty set is not a box, this procedure augments the uncertainty set and results in a loss of performance. Here, we mitigate this problem by tightly approximating the uncertainty set using the so-called sigma points and computing an ellipsoidal over-approximation of the reachable set of the system using the unscented transformation. We also improve the performance by considering the future reduction of the ranges of the uncertainties due to control actions and measurements thereby achieving implicit dual control actions. The advantages of the proposed approach over the standard multi-stage NMPC scheme are demonstrated for a linear and a nonlinear (semi-batch reactor) simulation case study.
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