Stochastic nonlinear model predictive control of a batch fermentation process

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Nonlinear model predictive control (NMPC) is an attractive control approach to regulate batch processes reliant on an accurate dynamic model. Most dynamic models however are affected by significant uncertainties, which may lead to worse control performance and infeasibilities, considering the tendency of NMPC to drive the system to its constraints. This paper proposes a novel NMPC framework to mitigate this issue by explicitly taking into account time-invariant stochastic uncertainties. Parametric uncertainties are assumed to be given by so-called polynomial chaos expansions (PCE), which constitutes a flexible approach to depict arbitrary probability distributions. It is assumed that at each sampling time only noisy output measurements are available. The proposed procedure uses a sparse Gauss-Hermite sampling rule to formulate an efficient scenario-based NMPC algorithm based on the PCE, while a stochastic nonlinear filter is employed to update the PCE given the available measurements. The framework is shown to be effective on a challenging semi-batch fermentation process simulation case study.