Robust Analysis and Parameters Identification of the Nonlinear Multistage Dynamical System in Batch Fermentation of Glycerol

This paper discusses a complex biological problem which is the fermentation of glycerol by Klebsiella pneumoniae in batch culture. We set up an improved multistage model involving the concentration of intracellular substances. Furthermore, the existence, uniqueness, and continuity of solutions with respect to the parameters are discussed. On the condition that glycerol and 1,3-propanediol are assumed to pass the cell membrane by passive diffusion coupled with facilitated transport, we take the relative errors between experimental data and computational values of the extracellular substances concentrations and the biological robustness of the intracellular substances concentrations as the performance index. Then we establish a parameter identification model and construct the particle swarm optimization algorithm to solve it. Finally, the numerical result shows that the improved model could describe the glycerol fermentation in batch culture well.