Modelling And Optimization Of A Class Of Nonlinear Enzyme-catalysis Hybrid System

This dissertation is based on the background of microbial production of1,3-propanediol (1,3-PD) using glycerol as substrate. In consideration of the uncertain metabolic mechanisms and the lack of intracellular experimental results in batch and continuous cultures, this disserta-tion studies the modelling, system identification, parameter sensitivity analysis and optimization of a class of nonlinear enzyme-catalytic hybrid system. Additionally, modelling and parameter optimization of a nonlinear switching hybrid system are investigated to describe the fed-batch fermentation process of glycerol with pH feedback. The main contributions are summarized as follows:1. A class of nonlinear enzyme-catalytic hybrid system is proposed to describe the batch fermentation process of glycerol under multiple possible transport mechanisms. Some basic properties of the hybrid system and its solution are also discussed. With the trans-port mechanisms as the discrete variables and the kinetic parameters as the continuous ones, a system identification model of the enzyme-catalytic hybrid system is established. This dissertation constructs a two-phase optimization algorithm on the basis of complex method together with fast simulated annealing technology, and deduces the most possible transport mechanism of1,3-PD.2. This dissertation proves the continuity of the parametric sensitivity functions of the enzyme-catalytic hybrid system of batch culture. A global parametric sensitivity anal-ysis approach is designed by combining the local technique with Monte Carlo method. With only those parameters of higher sensitivity as design variables, a parameter identifi-cation problem of the enzyme-catalytic hybrid system is presented. Finally, by using the first gradients of the constraints functions, we develop a gradient-based simulated anneal-ing algorithm to solve the parameter identification problem. Numerical calculations and simulations are carried out based on multiple groups of experiment results. 3. In this dissertation, a nonlinear enzyme-catalytic hybrid system corresponding to multi-ple possible transport mechanisms is established to describe the continuous fermentation of glycerol. Due to the lack of the intracellular experimental data, we quantitatively for-mulate the biological robustness of the metabolic system on the basis of the effect of the random parameter disturbances on the intracellular computational results to evaluate the reliability of the hybrid system. With the biological robustness as the performance index, a random system identification model of the enzyme-catalytic hybrid system is proposed. The decomposability and identifiability of the identification model are all proved. Finally, the dissertation constructs a numerical procedure and carries out numerical calculations under substrate-sufficient and substrate-limited conditions, respectively.4. A nonlinear state-based switching hybrid system is proposed to describe the coupled fed-batch fermentation with pH feedback. The dissertation discusses the non-Zeno and well-posedness of the hybrid system, presents its parametric sensitivity equations and proves the existence and uniqueness of the solutions. With the kinetic parameters of the hy-brid system as the designed variables, we establish a parameter identification model with continuous states inequality constraints. By constraint transcription and local smoothing technique, the identification problem is transformed to a traditional constraint nonlin-ear programming problems. Based on the parameter sensitivity functions, we derive the first gradients of the constraint functionals and the cost functional with respect to the pa-rameters and develop an dual descent optimization algorithm. Numerical results show the appropriateness of the proposed hybrid system and the validity of optimization algorithm.