Jinlong Yuan

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

Abstract 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.

Parameter identification for a nonlinear enzyme-catalytic dynamic system with time-delays

In this paper, we consider a nonlinear enzyme-catalytic dynamical system with uncertain system parameters and state-delays for describing the process of batch culture. Some important properties of the time-delay system are discussed. Taking account of the difficulty in accurately measuring the concentrations of intracellular substances and the absence of equilibrium points for the time-delay system, we define quantitatively biological robustness of the intracellular substance concentrations for the entire process of batch culture to identify the uncertain system parameters and state-delays. Taking the defined biological robustness as a cost function, we establish an identification model subject to the time-delay system, continuous state inequality constraints and parameter constraints. By a penalty approach, this model can be converted into a sequence of nonlinear programming submodels. In consideration of both the difficulty in finding analytical solutions and the complexity of numerical solution to the nonlinear system, based on an improved simulated annealing, we develop a parallelized synchronous algorithm to solve these nonlinear programming submodels. An illustrative numerical example shows the appropriateness of the optimal system parameters and state-delays as well as the validity of the parallel algorithm.

Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol

In this paper, we consider a nonlinear multi-stage dynamic system to characterize batch culture. We construct corresponding linear variational system for the solution to the multi-stage system, also prove the boundedness of fundamental matrix solutions for the linear variational system. On this basis, we prove strong stability with respect to perturbance of initial state vector for the multi-stage system through the application of such boundedness. From extensive simulation study, it is observed that the strong stability is highly satisfactory.

Strong stability of optimal design to dynamic system for the fed-batch culture

Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis (with few exceptions) is unable to provide general solutions; even the conditions to the existence of equilibrium point for the nonlinear dynamic system are simply not established in some special cases. In this paper, based on numerical solution of a nonlinear multi-stage automatic control dynamic (NMACD) in fed-batch culture of glycerol bioconversion to 1,3-propanediol (1,3-PD) induced by Klebsiella pneumoniae (K. pneumoniae), we consider an optimal design of the NMACD system. For convenience, the NMACD system is reconstructed together with the existence, uniqueness and continuity of solutions are discussed. Our goal is to prove the strong stability with respect to the perturbation of initial state for the solution to the NMACD system. To this end, we construct corresponding linear variational system for the solution to the NMACD system, and also prove the boundedness of fundamental matrix solutions to the linear variational system. On this basis, we prove the strong stability appearing above through the application of this boundedness.