Identification And Optimal Control Of Nonlinear Dynamical System In A Class Of Microbial Culture

1,3-propanediol(1,3-PD)is an important building block for industrial products,it can be used in the production of glue,antifreeze and polymers such as polytrimethylene terephthalate(PPT).The way with microbial fermentation is more eco-friendly than the chemical way to produce 1,3-PD.Therefore,this dissertation is based on the background of producing 1,3-PD with microbial fermentation,including the modelling,the analysis of robustness,the system identification and optimal control for a nonlinear hybrid system in batch culture and continuous culture.The results of this research can not only enrich the theory and the application of nonlinear dynamical systems,but also provide certainly guidance for the industrialization of 1,3-propanediol.The research was supported by the National Natural Science Foundation,National High-tech RD Program of China(863 Program)and the National Program on Key Basic Research Project(973 Program).The main conclusions about this dissertation can be summarized as follows.1.The bioconversion of glycerol to 1,3-propanediol is a complex bioprocess.We consider a nonlinear dynamical system with piecewise linear continuous functions as identification parameters to describe the batch culture.The basic properties of the dynamical system are proved,i.e.,the existence and uniqueness of solutions,Lipschitz continuity,uniform boundedness and strong stability with respect to different initial concentrations.Based on the relative deviation between computational results and the fitted curve which is obtained through the experimental data as performance index,an identification model is proposed with piecewise linear continuous functions as optimization variables.We also prove the identifiability and the existence of the optimal solution for the identification model,after that an optimization algorithm is constructed to solve the identification model.Numerical simulations are carried out though multiple groups of experiment data,it can be found that the present model can simulate the process of microbial fermentation very well.2.As the transport ways of glycerol and 1,3-PD across the cell membrane are still unclear in batch culture,we establish an enzyme-catalytic nonlinear hybrid system with piecewise linear continuous functions as identification parameters and involving 36 possible metabolic pathways.Considering the lack of experimental data on the concentration of intracellular substances,with biological robustness as performance index a complicated identification model for system pathways is established,involving 28800 system parameters and 72 pathway parameters.A parallel complex method is proposed to solve the optimization problem.Based on multiple groups of experiment data numerical simulations are carried out to determine the most reasonable transport systems of glycerol and 1,3-propanediol from all possible ones,which may offer some new insights on the the mechanism of microbial fermentation.3.During the process of producing 1,3-PD in microbial batch culture,it is crucial for increasing the production of 1,3-PD to use the appropriate proportion of the initial concentration of microbial and glycerol.On the basis of the optimal model in chapter four,an optimal control model is constructed with the maximize production of 1.3-PD at the terminal time as performance index and the initial concentration of glycerol and biomass as control parameters.We present an optimal control model which is subjected to continuous state inequality constraints with the initial concentration of glycerol and biomass as control parameters.A constraint transcription approach and a local smoothing technique are introduced to deal with the continuous state inequality constraints,then the gradient of constraint function with respect to the control parameters is obtained.Finally,a gradient-based simulated annealing optimization algorithm is constructed to solve the optimization parameter identification problem.Numerical results show that the production of 1,3-PD increase significantly at the terminal time.4.Considering many kinds of transport ways of glycerol and 1,3-PD in the process of producing 1,3-PD in microbial continuous culture,we construct a nonlinear hybrid dynamical system of genetic regulation in continuous culture.The state variables in this system involve the concentration of extracellular substances and intracellular substances,numerical results for the concentration of extracellular substances can be compared with the experimental data.Due to the lack of the intracellular substances experimental data,a novel quantitative definition of biological robustness is proposed to characterize the system.It not only considers the expectation of system output data after parameters disturbance but also considers the influence of the variance of these data.With the biological robustness as the performance index,an identification model of bi-level dynamical programming is established,involving 837 system parameters(optimization variables of down level)and 108 pathway parameters(optimization variables of up level).Then,we design a modified parallel particle swarm algorithm to solve the system identification model.Numerical results show that the most possible metabolic pathway is active transport coupling with passive diffusion for glycerol.