以函数为参量的间歇发酵非线性动力系统及其辨识

doi:10.15960/j.cnki.issn.1007-6093.2017.02.006

运筹学学报

以函数为参量的间歇发酵非线性动力系统及其辨识

杨琦^1,2,* 蒋志刚¹ 冯恩民¹ 尹洪超² 修志龙³

1. 大连理工大学数学与科学学院, 辽宁大连 116024; 2. 大连理工大学能源与动力学院, 辽宁大连 116024; 3. 大连理工大学生命科学与技术学院, 辽宁大连 116024

收稿日期:2016-09-12 出版日期:2017-06-15 发布日期:2017-06-15
通讯作者: 杨琦 E-mail: yangqi0028@163.com
基金资助:
国家自然科学基金青年基金(Nos. 11301051, 11301081, 11501574), 国家自然科学基金面上项目(Nos. 11171050, 10871033), 国家973计划项目(No. 2007CB714304), 国家863计划项目(No. 2007AA022208)

Nonlinear dynamic system of batch fermentation with the function as parameters and identification

YANG Qi^1,2,* JIANG Zhigang¹ FENG Enmin¹ YIN Hongchao² XIU Zhilong³

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China; 2. School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China;
3.School of Environmental and Biological Science and Technology, Dalian University of Technology, Dalian 116024, Liaoning, China

Received:2016-09-12 Online:2017-06-15 Published:2017-06-15

摘要/Abstract

摘要：

建立以连续分段线性函数为参量的间歇发酵非线性动力系统, 证明该动力系统的主要性质及解的存在性. 以实验数据拟合得到的光滑曲线为依据, 提出了连续分段线性函数为优化变量的辨识模型, 论述可辨识性. 依状态变量与辨识函数的相关性, 构造求解辨识模型的优化算法, 并给出优化算法的收敛性分析及数值结果.

关键词: 非线性动力系统, 连续分段线性函数, 辨识, 间歇发酵

Abstract:

In this paper, we propose a nonlinear dynamical system of batch fermentation with the continuous piecewise linear functions as parameters, and investigate the existence of solution about the nonlinear dynamical system. Based on a smooth curve which is fitted to the experimental data, a new identifiable model was established by using the continuous piecewise linear function as optimization parameters. According to the relationship between the state variables and identification function, an efficient algorithm is developed to solve the identification system, and the convergence of optimization algorithm is also analysed. Finally, numerical results are discussed to illustrate the validity of the present model.

Key words: nonlinear dynamic system, continuous piecewise linear function, identification, batch fermentation

杨琦, 蒋志刚, 冯恩民, 尹洪超, 修志龙. 以函数为参量的间歇发酵非线性动力系统及其辨识[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2017.02.006.

YANG Qi, JIANG Zhigang, FENG Enmin, YIN Hongchao, XIU Zhilong.

Nonlinear dynamic system of batch fermentation with the function as parameters and identification

[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2017.02.006.

参考文献

[1] Hermann B G, Patel M. Today's and tomorrow's bio-based bulk chemicals from white biotechnology: a techno-economic analysis [J]. Applied Biochemistry and Biotechnology, 2007, 136(3): 361-388.

[2] Eiteman M A, Lee S A, Altman E. A co-fermentation strategy to consume sugar mixtures effectively [J]. Journal of Biological Engineering, 2008, 2(1): 3.

[3] 修志龙. 微生物发酵法生产1,3-丙二醇的研究进展 [J]. 微生物学通报, 2000, 27(4): 300-302.

[4] 修志龙, 曾安平, 安利佳. 甘油生物歧化过程动力学数学模型和多态研究 [J]. 大连理工大学学报, 2000, 46(4): 428-433.

[5] Sun Y Q, Qi W T, Teng H, et al. Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: Concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane [J]. Biochemical Engineering Journal, 2008, 38(1): 22-32.

[6] Sun Y Q, Ye J X, Mu X J, et al. Nonlinear mathematical simulation and analysis of Dha Regulon for glycerol metabolism in Klebsiella pneumonia [J]. Chinese Journal of Chemical Engineering, 2012, 20(5): 958-970.

[7] 高彩霞, 王宗涛, 冯恩民. 微生物间歇发酵生产1,3-丙二醇过程的辨识与优化 [J]. 大连理工大学学报, 2006, 46(5): 771-774.

[8] 袁金龙, 冯殊伦, 冯恩民. 甘油间歇发酵酶催化非线性动力系统的强稳定性 [J]. 控制与决策, 2014, 29(08): 1505-1508.

[9] Lian H S, Feng E M, Li X F. Oscillatory behavior in microbial continuous culture with discrete time delay [J]. Nonlinear Analysis: Real World Applications, 2009, 10(5): 2749-2757.

[10] Wang J, Ye J X, Yin H C, et al. Sensitivity analysis and identification of kinetic parameters
in batch fermentation of glycerol [J]. Journal of Computational and Applied Mathematics, 2012, 236(9): 2268-2276.

[11] Zhai J G, Ye J X, Wang L, et al. Pathway identification using parallel optimization for a complex metabolic system in microbial continuous culture [J]. Nonlinear Analysis: Real World Applications, 2011, 12(5): 2730-2741.

[12] Wang G, Feng E M, Xiu Z L. Modeling and parameter identification of microbial bioconversion in fed-batch cultures [J]. Journal of Process Control, 2008, 18(5): 458- 464.

[13] Liu C Y, Gong Z H, Feng E M. Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture [J]. Journal of Industrial and Management Optimization, 2009, 5(4): 835-850.

[14] 李晓红, 冯恩民, 修志龙. 微生物间歇发酵非线性动力系统的性质及最优控制 [J]. 运筹学学报, 2005, 9(4):89-96.

[15] Elijah P. Optimization: Algorithms and Consistent Approximations [M]. New York: Springer, 1997.

以函数为参量的间歇发酵非线性动力系统及其辨识

Nonlinear dynamic system of batch fermentation with the function as parameters and identification

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