The Optimal Control Of The Nonlinear Impulsive System And Its Application

This dissertation studies the nonlinear differential dynamical systems and their optimal control problems with the bio-dissimilation of glycerol to 1,3-propanediol by klebsiella pneumoniae in the background. The contents include the nonlinear differential dynamical systems of the microbial continuous and batch cultures, the nonlinear impulsive system of fed-batch fermentation, their parameter identification models and optimal controls. The properties of the solution to the systems and their controllability are discussed. The main results can not only advance the develop of the theory and algorithm of impulsive differential equations and optimal control, but also reduce the experimental cost and provide certain reference for industrialization of 1,3-propanediol production by fermentation. So this study is very interesting in both theory and practice. The main results, obtained in this dissertation, may be summarized as follows:1. The nonlinear differential dynamic systems of continuous and batch fermentations to 1,3-propanediol by klebsiella pneumoniae are investigated. Considering big errors between the experimental results and computational values in the previous works, The parameter identification models for the systems are established. The existence of the solutions of the parameter identification models is proved and the necessary conditions of optimality are obtained. The feasible optimization algorithms are constructed to find the optimal parameters for the systems in accordance with the experimental results. According to the nonlinear dynamical system of the batch fermentation, the terminal optimal control model is established with the initial state as its control variable and the optimal solution is obtained according to an actual problem.2. The nonlinear impulsive dynamical system of fed-batch fermentation and its parameters identification problem are investigated in the process of bio-dissimilation of glycerol to 1,3-propanediol by klebsiella pneumoniae. A nonlinear impulsive dynamical system of the fed-batch culture and its parameters identification problem are proposed. The questions of existence, uniqueness and regularity properties of solutions for the impulsive system and the continuous dependence of solutions on initial values and the control variable are studied on the piecewise continuous spaces. Based on the compactness of the solution set of the system, the existence of the parameters identification problem and the necessary condition of optimality for the system are obtained. Thesensitivity matrix with respect to the model parameters is defined. Based on the sensitivity analysis of the parameters in the model, this paper constructs the optimization algorithm of the identification model on the sensitive parameters. The numerical simulations show that the errors between experimental and computational values using the impulsive system are less than those using the previous system. And the impulsive system presented in this paper is fit for formulating the factual fermentation better than the continuous models in being.3. The optimal control of the nonlinear impulsive dynamical system of the fed-batch glycerol fermentation is investigated. A terminal optimal control model are presented with the nonlinear impulsive system as its constraint condition and the existence of the optimal control is proved. The control variables here are the times of occurrence of impulses and the sizes of jumps in the states at the impulsive instants and the objective is to maximize the productivity of 1,3-propanediol over one cycle. Finally, an algorithm is constructed to solve the optimal control problem relying 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 can shorten the computational time. The optimal control model can provide theoretical reference for controllability of the process of 1,3-propanediol production by fermentation.