Research On A Class Of Impulsive Time-delay Optimal Control Problems And Its Applications

In this paper,parameter identification and optimal control of a class of nonlinear impulsive time-delay systems are studied in microbial fed-batch fermentation of glycerol to 1,3-propanediol(1,3-PD).According to the characteristics of fed-batch fermentation process,an eight-dimensional nonlinear impulsive time-delay dynamic system was established considering the trans-membrane transport modes of substrate and target product and the influence of intermediate metabolites on fermentation.The main contributions of the dissertation are summarized as follows:1.In the microbial fed-batch fermentation process,each alkali and glycerol injection process is very short and can be ignored compared with the whole fermentation process.Therefore,in this paper,the injection form of glycerol and alkali is regarded as an impulsive process,and the time-delay phenomenon of microbial growth is fully considered.A nonlinear impulsive time-delay dynamic system is proposed to describe fed-batch fermentation process.The existence and uniqueness of solutions for the nonlinear impulsive systems with time-delay and their continuous dependence on dynamic parameters and time-delay are proved.In order to determine the optimal parameters and time-delay of dynamic systems,a robust parameter identification model with continuous state inequality constraints was proposed by taking the weighted sum of the least square error between extracellular experimental data and calculated data and the biological robustness of intracellular materials as the performance index.The robust parameter identification problem is transformed into a set of optimization problems with only box constraints by constraint transformation technique and penalty function method.On this basis,we propose an improved parallel particle swarm optimization algorithm to solve this problem.Numerical results show that the least square error of the identified model is significantly lower than that of other literatures.This shows that the nonlinear impulsive time-delay dynamic system can describe fed-batch fermentation process reasonable,and the proposed algorithm is effective.2.Based on the established nonlinear impulsive time-delay system and the optimal time-delay and parameters,we present an optimal control problems,where the adding of alkli and glycerol is taken as the control function,1,3-PD concentration at the termial time as the performance index and the operation requirments as the continuous state inequality contraints.By introducing an exact penalty method,the optimal control problem is transformed into an optimization problem with only box constraints.On this basis,an improved differential evolution algorithm is proposed to solve the corresponding optimal control problem.The numerical results show that the concentration of 1,3-PD at the terminal time is increased significantly.