Optimization For The Enzyme-catalytic Nonlinear Time-delay System In Microbial Batch Culture

In view of the process of batch culture of glycerol bioconversion to 1,3-propanediol, this dissertation investigates an enzyme-catalytic nonlinear time-delay system, a corre-sponding optimal control model and gives the optimal control solution. This study can not only enrich the research of optimal control theory and algorithm as well as delay differential equation, but also provide basic theoretical reference for mass producing 1,3-propanediol. The main results obtained in this dissertation may be summarized as fol-lows.1. Based on the dynamic model of microbial batch fermentation, we set up an enzyme-catalytic nonlinear time-delay system in this dissertation. We assume that g-lycerol and 1,3-propanediol pass the cell membrane by passive diffusion coupled with facilitated transport, and introduce a time-delay into the concentrations of biomass. Fur-thermore, according to the ordinary differential equation theory and the relevant knowl-edge of optimal control, the existence, uniqueness, boundness and continuity of solutions with respect to the uncertain parameters are discussed.2. Due to the investigated nonlinear time-delay system, taking the productivity of 1,3-propanediol at terminal time as the cost function and the initial concentration of biomass, glycerol, and terminal time as the control vectors, we propose an optimal control model, and discuss the existence of the optimal control.3. To seek the optimum solution of the optimal control, a modified Nelder-Mead algorithm involved with the constraint transcription and smoothing techniques is then developed, and the optimal solution is also given. Finally, the optimization numerical re-sults illustrate that the terminal intensity of producing 1,3-propanediol has been increased obviously under the condition of using the optimal control. This work will provide basic theoretical reference for the optimal control in the process of batch culture producing 1,3-propanediol.