甘油连续生物歧化过程的状态反馈最优控制  

Optimal control for continuous bio-dissimilation process of glycerol with state feedback

作　　者：徐恭贤[1] 王雨竹[1] 李竹茜 XU Gongxian;WANG Yuzhu;LI Zhuxi(School of Mathematical Sciences,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《重庆理工大学学报（自然科学）》2022年第8期277-283,共7页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(11101051);辽宁省自然科学基金项目(20180550839);辽宁省教育厅科学研究项目(LJ2020015);辽宁省高水平创新创业团队支持计划项目(XLYC2008002)。

摘　　要：研究了甘油连续生物歧化过程的状态反馈最优控制。针对甘油连续生物歧化过程的非线性常微分方程动力系统,以最大化终端时刻目的产物1,3-丙二醇浓度为优化性能指标,提出了最优控制模型;通过设计线性部分状态反馈控制器,将最优控制模型转化为含反馈控制参数的动态优化问题。为了确定最优反馈控制参数,通过有限元配置形式将复杂的动态优化模型化为大规模非线性规划问题,并设计了带有多初始点策略的有效内点算法对其进行求解。通过计算得到最优反馈控制参数,实现了甘油连续生物歧化过程的状态反馈最优控制。最终获得的1,3-丙二醇浓度为546.121 499 mmol·L^(-1),是已有方法结果的1.279 463倍。Optimal control for continuous bio-dissimilation process of glycerol with state feedback was addressed. According to a dynamical system of ordinary differential equations on the continuous bio-dissimilation process of glycerol, an optimal control model was first proposed. This optimal control model can maximize the concentration of product 1,3-propanediol at final time. Then by designing a linear controller with partial state feedback, the optimal control model was turn into a dynamic optimization problem with feedback control parameters. A complex dynamic optimization problem should be solved to obtain the optimal feedback control parameters. So by the orthogonal collocation on finite elements, the complex dynamic optimization model was turn into a large-scale nonlinear programming. And the interior point approach with multiple initial point strategy was given to efficiently solve the attained nonlinear programming problem. After obtaining the optimal feedback control parameters, the optimal state feedback control for continuous bio-dissimilation process of glycerol was completed. The attained concentration of 1,3-propanediol is 546.121 499 mmol·L^(-1), which is 1.279 463 times the result of existing method.

关 键 词：生物歧化过程 最优控制 状态反馈 甘油 

分 类 号：O29[理学—应用数学]