Multi-stage Economic Nonlinear Model Predictive Control of bioreactors using dynamic flux balance analysis models

Dynamic Flux Balance Analysis (dFBA) models are powerful metabolic models that have a large potential for application in bioprocess control and optimisation. However, dFBA has an embedded linear FBA optimisation problem with degenerate solutions that give rise to multiple possible state trajectories that all satisfy the model. To address this uncertainty, we propose using a robust control approach based on Multi-stage Economic Nonlinear Model Predictive Control, which allows handling the degenerate solutions of the FBA problem without being too conservative. We propose to add a regularisation term to the FBA problem, to ensure a unique solution and generate the uncertainty scenarios by varying the regularization weights. The scenarios generated in that way then correspond to different solutions of the FBA problem. Then, the KKT conditions of the regularised FBA problem are imposed as equality constraints on the optimal control problem, which is solved using a direct collocation approach. Our methodology is evaluated through a case study on the optimal control of a fed-batch bioreactor for Escherichia coli growth, subject to a constraint on acetate concentration. The results demonstrate that the proposed MS-ENMPC approach, combined with the dFBA model, effectively satisfies the constraints despite uncertainties in the system trajectories. • Multiple state trajectories in dFBA models can impact ENMPC constraint satisfaction. • A Multi-stage ENMPC using dFBA models is proposed. • A quadratic regularisation of the FBA problem is used to generate scenarios. • The controller is demonstrated on a fed-batch bioreactor with E. coli .