Identification And Optimal Control Of Nonlinear Hybrid System In A Class Of Microbial Fermentation

This dissertation is based on the background of microbial production of1,3-Propanediol in the batch and fed-batch fermentation of glycerol by Klebsiella pneumoniae. This dissertation studies the modelling, system identification and optimization of this class fed-batch fermen-tation process. Additionally, based on qualitative heuristic knowledge from biochemists, the hybrid system modelling and identification of batch fermentation by using fuzzy system ap-proach is also studied. The research can not only develop nonlinear hybrid dynamical system, optimal control theory, optimization algorithm and the modeling method of unascertain system but also provide certain reference for commercial process of1,3-Propanediol by fermentation. Therefore, it is very interesting both in theory and in practice. The main contributions are summarized as follows:1. Considering the fed-batch fermentation process of glycerol coupled alkali, a nonlinear impulsive dynamical system is proposed to formulate this process. To obtain as much1,3-Propanediol as possible, an optimal control model involving the proposed impulsive system and subject to continuous state inequality constraints is then presented, in which impulsive instants and volumes of feeding glycerol and alkali are taken as control vari-ables. Subsequently the existence of the optimal control is proved. A solution approach is developed to seek the optimal impulsive strategies of glycerol and alkali based on gra-dient information. By numerical calculation, the optimal impulsive strategy of glycerol and alkali then are obtained.2. In this dissertation, a nonlinear hybrid dynamical system is proposed to formulate the fed-batch fermentation of glycerol by Klebsiella pneumoniae with open loop glycerol input and pH logic control. Some important properties of the solution to the proposed system are then discussed, including the existence, uniqueness, boundedness and regularity. To estimation the unknown parameters in the system, a parameter identification problem is proposed, and its identifiability is also proved. Subsequently, the parametric sensitivity functions of the system are given and utilized to obtain the requisite gradient information for further numerical computation. Finally a gradient-based algorithm to solve the identi-fication problem is constructed in conjunction with constraint transcription and smoothing approximation technique. Numerical simulations show the proposed hybrid system can describe the fed-batch culture properly.3. In this dissertation, a novel model for describing the process of glycerol batch fermenta-tion is proposed by incorporating qualitative heuristic knowledge from biochemists via a fuzzy expert system approach into Enzyme-catalysis dynamical system. Some important properties of the proposed system are then discussed. To determine the model parameters and membership functions, we establish a parameter identification model with the relative error of experimental data and simulating results as performance index, and demonstrate the existence of the optimal solutions of the identification model. An optimization algo-rithm is developed to solve the identification model based on improved particle swarm optimization and penalty function method. Finally, the numerical simulations show the validity of the proposed model and the effectiveness of the optimization algorithm.