Automatic design of robust model predictive control of a bioreactor via Bayesian optimization

Model predictive control (MPC) is an advanced control strategy that can deal with general nonlinear systems and constraints but relies on accurate predictions given by a dynamic model. To satisfy constraints and improve performance despite imperfect models, robust MPC methods can be formulated. Multi-stage MPC is a robust MPC method based on the formulation of scenario trees. The resulting optimization problems can be large, as the number of scenarios considered in the tree results from the combinations of all possible uncertainties. For systems with many uncertainties, as it is the case in bioprocesses, the optimization problems become rapidly intractable. To solve this issue, heuristics are typically used to select the most relevant uncertain parameters and their range of uncertainty. In this paper, we propose a two-step approach to obtain a systematic design of multi-stage MPC controllers: First, the key uncertain parameters are extracted based on the parametric sensitivities. Second, Bayesian optimization is employed for tuning of the range of uncertainties. The approach is applied to a bioreactor simulation study. The proposed approach can avoid constraint violations that are otherwise obtained by standard MPC while being less conservative than a manually-tuned robust controller.