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.Comment: Corrected typos in equatio

Stability Properties of the Adaptive Horizon Multi-Stage MPC

This paper presents an adaptive horizon multi-stage model-predictive control (MPC) algorithm. It establishes appropriate criteria for recursive feasibility and robust stability using the theory of input-to-state practical stability (ISpS). The proposed algorithm employs parametric nonlinear programming (NLP) sensitivity and terminal ingredients to determine the minimum stabilizing prediction horizon for all the scenarios considered in the subsequent iterations of the multi-stage MPC. This technique notably decreases the computational cost in nonlinear model-predictive control systems with uncertainty, as they involve solving large and complex optimization problems. The efficacy of the controller is illustrated using three numerical examples that illustrate a reduction in computational delay in multi-stage MPC.Comment: Accepted for publication in Elsevier's Journal of Process Contro