Multistage NMPC with on-line generated scenario trees: Application to a semi-batch polymerization process

We present a multistage NMPC scheme with adaptive on-line scenario-tree generation. The scenario tree is assembled from predictions of worst-case uncertainty realizations that are identified based on a first-order approximation of the process model. The key property of the presented approach is that the size of the resultant optimal control problems does not scale directly with the number of uncertain model parameters. We demonstrate the applicability of the approach with an industrially relevant semi-batch polymerization process under parametric model uncertainty and noisy, incomplete state measurements. By allowing to account explicitly for estimation errors, the presented approach yields increased robustness when compared to nominal NMPC and a standard multistage NMPC scheme. Moreover, we investigate a combination of the presented approach with on-line estimation of uncertain model parameters alongside approximation of their confidence region to reduce the uncertainty range and consequently mitigate unnecessary conservatism. The results show that adaptation of model and uncertainty range yields considerable economic benefits without impairing the attained level of robustness for the considered process.