Parameter Identification, Optimal Control Of The Impulsive Delay System And Their Application

Based on the process of batch and fed-batch culture of glycerol bioconversion to 1,3-propanediol and considering its characteristic and dynamic conduct, this dissertation proposes a nonlinear impulsive delay system and its parameter identification model and also discusses the main feature of this system and controllability. This study can not only accelerate the research of impulsive delay differential equation, but also provide basic theoretical reference for producing 1,3-propanediol. Therefore, this research work has important theoretical meaning and practical value. This work was supported by the National Nature Science Foundation of China (grant no. 10471014) and the tenth 5 years' projects of Science and Technology Administration of China (grant no. 2001BA708B01-04). The main results, obtained in this dissertation, may be summarized as follows.Depended on characteristics of the process of fed-batch culture, this dissertation proposes a nonlinear impulsive delay system and its parameter identification model, with introducing time delays into specific growth rate, consumption rate and formation rate. Existence and uniqueness of solution of the nonlinear impulsive delay system and identifiability of the parameter identification model are all discussed. The continuous dependence of solution with respect to time delays is proved. Based on genetic algorithm, an optimization algorithm is constructed for the identification model by means of a method of decomposing interval. The numerical simulations show that the errors between experimental and computational values using the modified system are less than those using the previous system. This means that the modified model which includes time delays is fit for formulating the factual fermentation better than the previous one without time delays.On the basis of having introduced time delays into the nonlinear impulsive dynamic system of fed-batch fermentation producing 1,3-propanediol, this dissertation proposes a terminal optimal control model, whose constraint condition is just the nonlinear impulsive delay system and control variables are the pulse times and the amount of jumps. The existence of optimal control is discussed. Based on the differential results of derivative of objective functional at pulse times and the amount of jumps, an optimization algorithm for this optimal control problem is constructed. This algorithm is relied on the method to solve the problem in one subinterval. Compared with the optimization algorithm based on Maximal principle, it is not necessary to solve the dynamical system on the whole interval in each iterative, which canshorten the computational time. The numerical optimization results show that the terminal intensity of producing 1,3-propanediol has been increased obviously under the condition of using the optimal control. That work will provide basic theoretical reference for the control's achievement in the process of fed-batch culture producing 1,3-propanediol.