Optimal control of a nonlinear state-dependent impulsive system in fed-batch process  

作　　者：Chongyang Liu Guoqing Shi Gang Liu Dianzhong Hu 

机构地区：[1]School of Mathematics and Information Science Shandong Technology and Business University Yantai 264005,P.R.China [2]School of Computer Science and Technology Shandong Technology and Business University Yantai 264005,P.R.China [3]Yantai Haiyi Software Co.,Ltd.Yantai 264000,P.R.China

出　　处：《International Journal of Biomathematics》2023年第8期297-324,共28页生物数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12271307);the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019MA031).

摘　　要：Optimal control technique is crucial to improve the yield of microbial fermentation production.In this paper,we propose a nonlinear control system with state-dependent impulses,where the impulsive volume of feeding glycerol and the critical concentration of glycerol for occurring impulse are the control variables,to formulate 1,3-propanediol(1,3-PD)fed-batch production process.We also discuss a quantity of important properties for this control system.Then,we analyze the sensitivity of system state with respect to the kinetic parameters.We further propose a constrained optimal control model governed by the control system with state-dependent impulses.The existence of the optimal impulsive controls is established.For solving this problem,we utilize an exact penalty method to transform the problem into an optimization problem with only box constraints.Moreover,an improved differential evolution method is developed to seek the optimal impulsive strategy.Finally,numerical simulation results demonstrate that,by using the optimal impulsive strategies,final 1,3-PD concentration is considerably increased under the nominal parameter values and disturbances of kinetic parameters have significant effects on the optimal final 1,3-PD yield.

关 键 词：State-dependent impulsive system sensitivity analysis optimal control differential evolution fed-batch culture 

分 类 号：O175[理学—数学]