Robust estimation and economic predictive control for dynamic metabolic flux systems under probabilistic uncertainty

Abstract

A novel formulation is proposed for propagating parametric uncertainty for Dynamic Metabolic Flux models involving the solution of Linear Programming (LP) problems. The propagation approach is based on the calculation of all possible active sets of constraints at each time interval. Then, a tree-based approach is used to propagate the uncertainty onto the worst case of each active set where each branch of the tree corresponds to an active set of constraints. Each branch is assigned a relative probability according to the relative hypervolume occupied by the active set solutions in the parameter space. The approach is applied for the robust estimation of the Ecoli fermentation process and for the design of a robust economic predictive controller for this system. The proposed method is found to be significantly more efficient as compared with other uncertainty propagation approaches such as Monte Carlo (MC) simulations.