Modeling, Optimization And Optimal Control Of Several Problems In Microbial Fermentation

1,3-propanediol(1,3-PD) is an important chemical raw material.In recent years,the production of 1,3-PD by microbial fermentation has been widely investigated.The dissertation investigates the modeling,optimization and optimal control of several problems in glycerol bioconversion to 1,3-PD by Klebsiella pneumoniae(K.pneumoniae).The research not only can enrich the theory and the application of nonlinear dynamical systems, optimal control,bilevel programming and optimization theory and algorithm,but also can provide theoretical guide for the commercial production of 1,3-PD.Hence,this research is very interesting in both theory and practice.In addition,the research is supported by national natural science foundation,"973 program" and "863 program".The main contributions are summarized as follows:1.According to the characteristic of microbial growth in batch culture,we establish a controlled dynamical system with parameters to formulate this process by taking the total inhibitions of substrate and multiple products to the cell growth as the control function.Subsequently,some properties of the proposed system are proved. Taking the minimal error between the experimental data and calculated values as the performance index,and the above controlled dynamical system as the constraint, we present a system identification model,which is an optimal control problem.It is difficult to solve the system identification model directly.So,we transform it into a parameter identification problem by discretizing technique combining the characteristic of microbial growth.Finally,an improved particle swarm algorithm is constructed to obtain a satisfactory solution of the system identification problem. Numerical results show that the above algorithm is of good convergence and the errors are cut down by 6%-16%. 2.In view of the actual fed-batch fermentation process,we firstly propose a nonlinear multistage dynamical system,taking the feeding of glycerol and alkali as a time-continuous process instead of an impulsive form,to formulate the process.To determine the parameters in the multistage system,we establish a parameter identification model and prove the identifiability of optimal parameters.Finally,an improved simplex method is constructed to solve the identification model.Numerical results show that the error is cut down greatly and the proposed system can formulate the fed-batch culture better.Since a proper feeding rate is required during the fed-batch process,we propose a controlled multistage dynamical system by taking the feeding rate as the control function.Some important properties of the system are also proved.To maximize the productivity of 1,3-PD at the terminal time,an optimal control model subject to our proposed controlled multistage system and continuous state inequality constraints is presented.Finally,we obtain an optimality condition for the optimal control problem by non-differentiable optimization theory,and prove the equivalence between the optimality condition and zeros of the optimality function.3.Flux balance analysis(FBA) is an effective tool in the analysis of metabolic network. It can predict the flux distribution of engineered cells,whereas the accurate prediction depends on the reasonable objective function.Basing on the metabolic network,we firstly propose a nonlinear bilevel programming model to infer the metabolic objective function of anaerobic glycerol metabolism by K.pneumoniae for 1,3-PD production.Making use of the K-K-T optimality condition of the lower level problem,the bilevel programming model is equivalently transcribed into a nonlinear programming with complementary and slackness conditions.We give the existence theorem of the optimal solution to the above model.An efficient algorithm is proposed to solve the model and its convergence is also simply analyzed.It is necessary to investigate the robustness of the obtained objective function because of the experimental errors.Hence,a series of nonlinear bilevel programming models is established to analyze the robustness.Numerical results show that the obtained objective function is of good robustness.