| This dissertation investigates the nonlinear dynamical systems and their optimal control problems in fed-batch fermentation of glycerol bioconversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae. The research can not only develop nonlinear dy-namical system, optimal control theory and optimization algorithm, but also increase the productivity of product and provide certain reference for commercial process of 1,3-PD by fermentation. Therefore, it is very interesting both in theory and in practice. In addition, the research is supported by the National Natural Science Foundation of China, the Major State Basic Research Development Program of China and the National High Technology Research and Development Program of China. The main contributions obtained in this dissertation are summarized as follows.1. Taking the feeding of glycerol and alkali as a time-continuous process, we propose a nonlinear multistage dynamical system, in which the feeding rate of glycerol is the control function, to describe the microbial fed-batch fermentation of glycerol to 1,3-PD. Some properties, i.e., the existence and uniqueness, Lipschitzian conti-nuity in control function and uniform boundedness of solutions to the system, are proved. To maximize the concentration of 1,3-PD at the terminal time, a multistage optimal control model is presented. The existence of optimal control is established using theory of bounded variation. Based on the discretization method and an im-proved Particle Swarm Optimization algorithm, a global optimization algorithm is constructed to seek the optimal solution. Numerical results show that, by employing the optimal control policy, the concentration of 1,3-PD at the terminal time can be increased by 16.04% compared with the experimental data.2. It is decisive for improving the productivity of 1,3-PD to optimize the switching instants between the feeding and batch processes in microbial fed-batch fermen- tation. Thus, an autonomous switched system with variable switching instants is proposed to formulate the fermentation process. To maximize the concentration of 1,3-PD at the terminal time, we present an optimal control model involving the autonomous switched system and subject to continuous state constraints. A con-straint transcription approach and a local smoothing technique are introduced to deal with the continuous state inequality constraints. On the basis of a penalty function and the first and second gradients of the cost function, a gradient-based algorithm is developed to solve the optimal control model. Numerical results show that the concentration of 1,3-PD at the terminal time can be increased considerably compared with previous results.3. The feeding of glycerol should be kept in a given range such that it can not only provide sufficient nutrition for cells growth but also effectively avoid the inhibitory effect of excessive glycerol on the cells growth. A switched system with state depen-dent switching, in which the feeding rate of glycerol is taken as the control function, to describe the microbial fed-batch fermentation process. Some properties such as the existence and uniqueness, uniform boundedness, uniformly Lipschitzian conti-nuity and regularity of solutions, are discussed. To maximize the concentration of 1,3-PD at the terminal time, an optimal switching control model is presented. The existence of optimal control is also ascertained. Since the number of switchings is not known a prior. The optimal switching control model is equivalently transcribed into a two-level optimization problem. Finally, a solution method is developed on the basis of a heuristic approach and the control parametrization method. Numerical results show that, by employing the obtained optimal strategy,1,3-PD concentration at the terminal time can be increased considerably and the number of switchings is also decreased greatly. This provides guidance to the actual industrial production of 1,3-PD which is beneficial to optimize the biochemical engineer.
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