连续发酵过程分数阶非线性时滞最优控制  

Optimal Control of Fractional Nonlinear Time-delay System in Continuous Fermentation Process

作　　者：纪燕 翟金刚 冯恩民[2] JI Yan;ZHAI Jingang;FENG Enmin(School of Mathematics and Statistics Science,Ludong University,Yantai 264039,China;School of Mathematical Science,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]鲁东大学数学与统计科学学院,山东烟台264039 [2]大连理工大学数学科学学院,辽宁大连116024

出　　处：《鲁东大学学报（自然科学版）》2023年第4期352-359,共8页Journal of Ludong University:Natural Science Edition

基　　金：山东省自然科学基金(ZR2014FM029)。

摘　　要：针对连续发酵甘油转化1,3-丙二醇(1,3-PD)的过程可能存在的时滞现象,考虑用分数阶时滞系统描述发酵过程,讨论系统状态关于参数的灵敏度。以甘油稀释速率和注入浓度为优化变量,以使灵敏度函数值较小为约束条件,以及使终端时刻1,3-PD浓度最大为性能指标,构建分数阶时滞系统最优控制模型。利用协态方法,得到性能指标和约束关于优化变量及参数的梯度,构造了基于序列二次规划(SQP)方法的优化算法。数值结果验证了优化策略的有效性。Considering that there may be a time-delay in the conversion of glycerol to 1,3-propanediol(1,3-PD) in continuous culture,a fractional order time-delay system is considered to describe the fermentation process,and the sensitivity of system states with respect to the parameters is discussed.The optimal control model of the fractional time-delay system for the continuous fermentation was formulated with a small sensitivity as the constraint,the glycerol dilution rate and feeding concentration as the optimization variable,and the maximum concentration of 1,3-PD at the terminal time as the performance index.By using the co-state method,the gradients of performance index and constraints with respect to optimization variables and parameters were obtained,and a optimization algorithm based on sequential quadratic programming(SQP) method was constructed.Finally,the numerical results were used to verify the effectiveness of the optimization strategies.

关 键 词：分数阶导数 最优控制 时滞 连续发酵 

分 类 号：O224[理学—运筹学与控制论]