Robust Analysis And Parameter Identification Of A Enzymatic Nonlinear Dynamical System

In view of the microbial conversion batch fermentation of glycerol to1,3-propanediol, we establish a class of enzyme nonlinear dynamic system to characterize the batch fer-mentation of glycerol to1,3-PD by Klebsiella pneumoniae. We suppose that glycerol is transported from extracellular to intracellular as the combination of active transport and passive transport and that1,3-PD is transported from intracellular to extracellular as passive transport. The main contributions are summarized as follows:1. The existence, uniqueness and boundedness of solutions to the system and the continuity of solutions with respect to the parameters are discussed.2. It is difficult to measure the concentrations of intracellular substances; so. in view of the qualitative description of the biological robustness given by Jiang and Kitano, we put forward a newly quantitative definition of robustness index of the intracellular substances in terms of superior limit representation.3. Taking the robustness of intracellular substance concentrations as the performance index, an identification problem is proposed, which is subjected to the constraint of the en-zyme nonlinear dynamical system. In addition, we prove the identifiability of the proposed identification problem.4. We construct an optimization algorithm to solve the parameter identification mod-el and prove some convergence properties of the constructed optimization algorithm, and optimal parameters of the system are also given by the initial value of the solutions to the dynamical system of batch cultures which was derived from four groups practical experi-ments. Numerical results not only show that the established model can be used to describe the batch fermentation reasonably, but also imply that the optimization algorithm is valid.