A Class Of Nonlinear Impulsive Optimal Controls And Its Applications In Microbial Fermentation

1,3-Propanediol(1,3-PD)is a significant organic compound.Microbial fermentation is an effective and green process to produce 1.3-PD.The fed-batch method has been extensively utilized in industrial production.In this thesis,based on the process of 1,3-PD production by microbial fed-batch fermentation,the optimal control of a class of nonlinear state-dependent impulsive systems is studied.The contents of this thesis are:1.In the process of fed-batch fermentation,the impulse of glycerol and alkali will occur to provide sufficient nutrition when the concentration of glycerol reaches the critical value.Based on this,a nonlinear state-dependent impulsive control system is proposed to describe this process,in which the volume of injected glycerol in the fed-batch process and the critical concentration of glycerol when the impulse occurs are taken as control variables.Some important properties of the control system are discussed.Then,the sensitivity of the system state to the kinetic parameters is analyzed.Furthermore,taking the yield of 1,3-PD as performance index,an optimal impulsive control model with continuous state inequality constraints is also proposed,and the existence of optimal impulsive control is proved.In addition,the exact penalty function method is used to transform the problem into a penalty problem with only box constraints.To solve this problem,an improved differential evolution method is developed to find the optimal impulsive strategy.The effectiveness of the proposed algorithm is assessed through numerical examples.Furthermore,the optimal impulsive control problem is solved by applying the improved differential evolution algorithm.Finally,numerical simulation results show that,by using the optimal impulsive strategy,the yield of1,3-PD is significantly increased under the nominal parameter value,and the disturbance of the kinetic parameters has significant effects on the optimal final 1,3-PD yield,which also shows the effectiveness of the improved algorithm.2.Considering the time-delay phenomenon in the actual fermentation process,a statedependent time-delay impulsive system is proposed to describe the process of 1,3-PD production in fed-batch fermentation.In view of the uncertain kinetic parameters in fed-batch fermentation,a robust optimal control problem is proposed,where the impulse volume of injection and the critical concentration of glycerol of impulse occurrence are taken as the control variables,and the 1,3-PD yield as well as the sensitivity of the yield with respect to the kinetic parameters are regarded as the objective functions.The problem is transformed into a penalty problem only with box constraints by constraint transcription technique.As a result,an optimization algorithm is designed to solve the transformed penalty problem.The numerical results show that when the sensitivity is taken into account,the robustness of the system is greatly improved,while the production of 1,3-PD is not significantly affected.