# Metabolic Reaction Network-Based Model Predictive Control of Bioprocesses
###### Abstract  
Bioprocesses are increasingly used for the production of high added value products. Microorganisms are used in bioprocesses to mediate or catalyze the necessary reactions. This makes bioprocesses highly nonlinear and the governing mechanisms are complex. These complex governing mechanisms can be modeled by a metabolic network that comprises all interactions within the cells of the microbial population present in the bioprocess. The current state of the art in bioprocess control is model predictive control based on the use of macroscopic models, solely accounting for substrate, biomass, and product mass balances. These macroscopic models do not account for the underlying mechanisms governing the observed process behavior. Consequently, opportunities are missed to fully exploit the available process knowledge to operate the process in a more sustainable manner. In this article, a procedure is presented for metabolic network-based model predictive control. This procedure uses a combined moving horizon-model predictive control strategy to monitor the flux state and optimize the bioprocess under study. A CSTR bioreactor model has been combined with a small-scale metabolic network to illustrate the performance of the presented procedure. model predictive control; moving horizon flux estimation; metabolic network models; bioprocess optimization; online state and parameter estimation; dynamic metabolic flux analysis +
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of differential states. Therefore, the current state of the art in model-based bioprocess optimization relies on macroscopic mass balance models. This is one of the main reasons the current state of the art in model-based bioprocess optimization and control relies on macroscopic mass balance models, often only including biomass, substrate, and product mass balances. Macroscopic mass balance models make abstraction of the underlying mechanisms governing the studied bioprocess and therefore miss opportunities in achieving a better process monitoring and control. As there is no need to account for irrelevant parts of the metabolism for the process under study, genome-scale metabolic networks can be reduced to low complexity metabolic network models. The complexity of the metabolic network that should be used for a studied bioprocess depends on the level of detail required and the amount of experimental data or information available to identify the network. Hence, low- or medium-complexity metabolic networks can be used to account for the relevant intracellular mechanisms governing the bioprocess under study. Results from literature, e.g., [3], indicate that including such metabolic network models in bioprocess optimization results in an improved process performance compared with the use of an unstructured macroscopic bioprocess model. In addition, the intracellular fluxes can be estimated rather accurately from extracellular measurements using a low- or medium-complexity metabolic network as in e.g., [4; 5; 6; 7; 8], enabling an enhanced bioprocess monitoring by monitoring the flux state, hence the metabolic state of the microorganisms in the biochemical process. The current state of the art in model-based bioprocess control is model predictive control (MPC) in which a process model is used to solve an open-loop dynamic optimization problem over a time interval, called the prediction horizon to optimize the future of a process. The optimal control inputs are computed until a new measurement becomes available. In biochemical processes, not all states can be measured and the states need to be estimated from the available measurements. For linear systems a Kalman filter can be used to retrieve an optimal state estimate [9]. For nonlinear systems extended Kalman filter [10] or the unscented Kalman filter [11] can be used. Alternatively, moving horizon estimation (MHE) can be used which solves a constrained optimization problem based on a set of measurements obtained at previous time points and also moves this estimation horizon when a new measurement is obtained [12; 13; 14].