Nonlinear Dynamical Systems And Their Optimal Control In Bio-dissimilation

This dissertation investigates the nonlinear dynamical systems and their optimal control problems with the bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae in the background. Two different kinds of nonlinear dynamical systems are presented to describe the batch and the fed-batch fermentation. Properties of these systems and their parameters identification problem are discussed as well. Moreover, in order to find the optimal control strategy we propose optimal control models and obtain optimality conditions. These results can not only develop the theory and the application of nonlinear dynamical systems and optimal control, but also reduce experimental cost and provide certain guidance for industrialization of 1,3-propanediol production. Therefore, this research is very interesting in both theory and practice. The main results, obtained in this dissertation, are summarized as bellow:1. The batch fermentation of glycerol to 1,3-Propanediol could be divided into three stages according to the growth habit of Klebsiella pneumoniae, which are development stage, growth stage and steady stage, and on different stage the dynamical system is different as well. Using this property, we employ a nonlinear multistage dynamical system to describe batch fermentation and discuss the existence and uniqueness of solution to system. In order to identify values of parameters of this system such that the model can simulate the fermentation as exactly as possible, a parameters identification model is proposed and the existence of optimal solution is proved. Then an optimization algorithm is constructed to solve this problem. Numerical results show that errors between experimental and computational results are less than before, which implies that the nonlinear multistage dynamical system is fit for simulating such fermentation.2. The hybrid dynamical system of fed-batch fermentation and its parameters identification problem are investigated. Since there are continuously dynamic behavior and discrete events in the process of fed-batch fermentation of glycerol to 1,3-Propanediol, we propose a hybrid dynamical system to describe this kind of fermentation. The existence of solution to system together with the dependence of solution to parameters is discussed. Moreover, a parameters identification model is developed and an optimization algorithm is constructed to solve this parameters identification problem. Numerical results show that the average relative error of computational and experimental results of this system is only 1.9%, but that of the other system is 18.36%, which demonstrates that hybrid system has much advantage in describing fed-batch fermentation.3. Optimal control problems of the nonlinear multistage dynamical system and the nonlinear impulsive dynamical system are investigated. For batch fermentation, we present an optimal control model in which control variable is initial state and the nonlinear multistage dynamical system is constraint condition. The existence of solution to control model is discussed and the optimality condition is obtained. Then we propose an optimal control model for fed-batch fermentation, where volume of glycerol adding at impulsive moments are control variables and nonlinear impulsive dynamical system is constraint condition. The optimality condition of this problem is obtained as well. Furthermore, an optimal control problem with hybrid dynamical system as constraint condition is investigated and an optimization algorithm is constructed. Numerical result shows that the intensity of production of glycerol at terminal moment is improved from 38.448mmol/(L·h) to 42.13mmol/(L·h), which shows that the optimal control is necessary. The result provides guidance for the industrialization of 1,3-propanediol production by fermentation.