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运筹学学报 >

2017 , Vol. 21 >Issue 2: 46 - 56

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2017.02.006

运筹学

以函数为参量的间歇发酵非线性动力系统及其辨识

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  • 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

  网络出版日期: 2017-06-15

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)

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

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  • 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 date: 2016-09-12

  Online published: 2017-06-15

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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

本文引用格式

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, 2017 , 21(2) : 46 -56 . DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.006

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

参考文献

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