微生物发酵非线性动力系统的鲁棒次优控制
Robust Suboptimal Control of a Nonlinear Dynamical System in Microbial Continuous Fermentation
DOI: 10.12677/DSC.2013.22008, PDF, 下载: 3,007  浏览: 11,251  国家自然科学基金支持
作者: 王娟*：中国石油大学(华东)理学院，青岛；冯恩民：大连理工大学数学科学学院，大连；修志龙：大连理工大学环境与生命科学学院，大连
关键词: 非线性动力系统；系统灵敏度；鲁棒次优控制；微生物发酵；Nonlinear Dynamical System; System Sensitivity; Robust Suboptimal Control; Microbial Fermentation
摘要: 以微生物连续发酵为研究背景，讨论了带有不确定参数的非线性动力系统的一类最优控制问题。综合考虑了两方面的因素，一是生产强度极大化，二是生产强度对系统参数不确定性的灵敏度的极小化。讨论了非线性动力系统及其伴随动力系统的一些重要性质，证明了最优控制的存在性，并构造算法进行了数值求解。
Abstract: In this paper, taking the microbial continuous fermentation process as background, we discuss a class of optimal control problem of a nonlinear dynamical system with a set of scalar parameters which could have some uncertainty as to their exact values. Two factors are considered: one is maximizing the productivity, the other is minimizing the sensitivity of the productivity with respect to the uncertainty of the parameters. Some important properties of the nonlinear dynamical system and its adjoint system, and the existence of the optimal control are also proved. Numerical algorithm and results are given at the end.
文章引用：王娟, 冯恩民, 修志龙. 微生物发酵非线性动力系统的鲁棒次优控制[J]. 动力系统与控制, 2013, 2(2): 44-50. http://dx.doi.org/10.12677/DSC.2013.22008

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