Handling nonlinearities and uncertainties of fed-batch cultivations with difference of convex functions tube MPC

Bioprocesses are often characterized by nonlinear and uncertain dynamics. This poses particular challenges in the context of model predictive control (MPC). Several approaches have been proposed to solve this problem, such as robust or stochastic MPC, but they can be computationally expensive when the system is nonlinear. Recent advances in optimal control theory have shown that concepts from convex optimization, tube-based MPC, and difference of convex functions (DC) enable stable and robust online process control. The approach is based on systematic DC decompositions of the dynamics and successive linearizations around feasible trajectories. By convexity, the linearization errors can be bounded tightly and treated as bounded disturbances in a robust tube-based MPC framework. However, finding the DC composition can be a difficult task. To overcome this problem, we used a neural network with special convex structure to learn the dynamics in DC form and express the uncertainty sets using simplices to maximize the product formation rate of a cultivation with uncertain substrate concentration in the feed. The results show that this is a promising approach for computationally tractable data-driven robust MPC of bioprocesses.