Switching Optimal Control Of Nonlinear Hybrid Dynamical Systems In Microbial Continuous Fermentation

For a class of the microbial continuous fermentation process of glycerol to 1,3-propanediol(1,3-PD),the different levels of nonlinear switched systems are established in this dissertation.Based on the proposed sensitivity function and robustness index,we established different optimal control models,in which the product of 1,3-PD at the terminal time is taken as cost index.And some optimization algorithms are used to solve the models.Numerical results provided a reference for biochemical experiments.The main achievements are summarized follows.1.Considering both extracellular and intracellular environments,we propose a nonlinear switched system composed of 16 modes to model the microbial continuous fermentation process.Considering the parts of the system parameters depend on the decision variables,the sensitivities of the system states with respect to the parameters and the decision variables are discussed,and the gradient formulas containing switches are obtained.A switching optimal control model is formulated based on the sensitivity functions,in which the sequential quadratic programming(SQP)is applied for seeking numerical solution.Numerical results show that,by employing the optimal control strategies,the concentration of 1,3-PD at the terminal time can be increased considerably.2.Considering the parts of the system parameters depend on the decision variables,a quantitative robustness for the system parameters is given.We take the productivity of 1,3-PD at the steady-state time as cost index,and establish an optimization model,in which dilution rate and feeding concentration of glycerol are regarded as decision variables.By applying of the local smoothing approximation technique,the optimal control problem is approximated as a nonlinear mathematical programming problem.Finally,a numerical optimization algorithm containing switch is constructed for obtaining an optimal numerical solution of the considered problem.Numerical results indicate that the obtained optimal inputs,identified parameters,switching instants and mode sequence have perfect satisfaction than ever.3.According to the genetic regulation of dha regulon,we establish a switched system which is represented by a fourteen-dimensional nonlinear dynamical equation containing.We are committed to maximize the productivity of target product 1,3-PD at the terminal time by optimizing dilution rate and feeding concentration of glycerol which are regarded as decision variables.In view of the correlation between some unknown system parameters and the decision variables,we survey a quantitative description of biological robustness,and formulate an optimal control model based on robustness index.Then,effective algorithms are presented based on Exact Penalty Method and Simplex Search Method to solve the above optimization problem.We conclude that the obtained optimal strategies and state trajectories are reasonably satisfied by numerical simulations.