| 一种非线性多阶段动力系统的最优控制及数值优化 |
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| 引用本文： | 姜永,李艳杰,冯恩民,修志龙.一种非线性多阶段动力系统的最优控制及数值优化[J].生物数学学报,2010(4):616-622. |
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| 作者姓名： | 姜永 李艳杰 冯恩民 修志龙 |
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| 作者单位： | [1]大连理工大学数学科学院,辽宁大连116024 [2]沈阳航空航天大学理学院,辽宁沈阳110136 [3]大连理工大学生物工程系,辽宁大连116024 |
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| 基金项目： | 国家自然科学基金资助项目（编号为：10471014 10671126 10871033）;国家自然科学青年基金资助项目（编号为：11001180）; 国家“973”计划项目（编号为：2007CB714304）; 国家“863”项目（编号为;2007AA022208） |
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| 摘 要： | 针对间歇发酵过程的非线性多阶段动力系统,建立了以初始浓度为控制变量、以生产强度为性能指标的最优控制模型.证明了非线性多阶段动力系统的主要性质、最优控制的存在性及达到最优解的必要条件.构造了优化算法并应用于实际数据计算,其数值结果表明了本文模型与算法的有效性.
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| 关 键 词： | 非线性多阶段动力系统 最优控制 微生物发酵 |
The Optimal Control and Numerical Optimization of a Class of Nonlinear Multi-Stage Dynamical System |
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| JIANG Yong,LI Yan-jie,FENG En-min,XIU Zhi-long.The Optimal Control and Numerical Optimization of a Class of Nonlinear Multi-Stage Dynamical System[J].Journal of Biomathematics,2010(4):616-622. |
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| Authors: | JIANG Yong LI Yan-jie FENG En-min XIU Zhi-long |
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| Institution: | 1 School of Mathematical Sciences Dalian University of Technology,Dalian Liaoning 116024China) (2 Faculty of Science Shenyang Aerospace University,Shenyang Liaoning 110136 China) (3 Faculty of Biological engineering Dalian University of Technology,Dalian Liaoning 116024 China) |
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| Abstract: | In this paper we consider a class of nonlinear multi-stage dynamical system in batch fermentation and some properties of it.Based on this system,an optimal control model is proposed where the initial state is considered as control variable and the objective is to maximize the production intensity of 1,3-Propanediol at terminal moment.We prove existence of optimal controls and obtain the necessary condition for them.Furthermore,a optimization algorithm is developed.Numerical result shows that both the nonlinear multi-stage dynamical system and the optimization algorithm are effective. |
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| Keywords: | The nonlinear multi-stage dynamical system Optimal control Microbial fermentation |
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