Robust nonlinear model predictive control of a batch bioreactor using multi-stage stochastic programming

This paper presents a robust nonlinear model predictive control scheme and its application to a batch bioreactor. The approach is based on the description of the uncertainty evolution as a scenario tree. This makes it possible to take explicitly into account the future disturbances and control inputs leading to a non-conservative approach that is not based on the tracking of a nominal solution. The main challenge of the approach is that the size of the resulting optimization problem grows exponentially with the prediction horizon and with the number of uncertainties. The potential of the approach is demonstrated by simulation examples of a nonlinear penicillin fermentation process where the proposed scheme can fulfill the state and the input constraints for all the possible values of several uncertain parameters, improving the performance of existing robust approaches such as tracking of the necessary conditions of optimality.