Robust identification of enzymatic nonlinear dynamical systems for 1,3-propanediol transport mechanisms in microbial batch culture

In this paper, in view of glycerol bioconversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae), we study an enzyme-catalytic nonlinear dynamic system with uncertain parameters for formulating the process of batch culture. Some important properties are also discussed. Taking account of the difficulty in accurately measuring the concentrations of intracellular substances and the absence of equilibrium point of the nonlinear system in batch culture, a novel approach is used here to define quantitatively biological robustness of the intracellular substance concentrations for the overall process of batch culture. The purpose of this paper is to identify these uncertain parameters. To this end, taking the defined biological robustness as a performance index, we establish an identification model, which is subject to the nonlinear system. Simultaneously, the existence of optimal solution to the identification model is deduced. We develop an optimization algorithm, based on novel combinations of Nelder–Mead algorithm and the change rate of state variable, for solving the identification model under various experiment conditions. The convergence analysis of this algorithm is also investigated. Numerical results not only show that the established model can be used to describe the process of batch culture reasonably, but also imply that the optimization algorithm is valid.