Robust identification and its properties of nonlinear bilevel multi-stage dynamic system

In this paper, based on the microorganism batch fermentation of glycerol to 1,3-propanediol, we study a kind of nonlinear multi-stage dynamic system for the batch fermentation and its properties. Since it is difficult to measure the concentration of intracellular substance so far, we quantitatively describe robustness according to the basic features of biological systems. Taking experimental data of the concentration of extracellular substance and robustness as the performance index, we establish identification model of dynamic system for the batch fermentation. Then, its identifiability, the existence and continuity with respect to the parameters of the solution have been discussed. We decompose the identification problem into bilevel multi-stage optimal control subproblem, and both of them are equivalent. This work is a theoretical foundation of further numerical calculation.