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,    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

参考文献

[1] 修志龙. 1,3-丙二醇的微生物法生产分析[J]. 现代化工, 1999, 3: 33-35.
[2] H. Biebl, et al. Microbial production of 1,3-propanediol. Applied Microbiology and Biotechnology, 1999, 52: 289-297.
[3] A. P. Zeng, et al. Multiple product inhibition and growth model- ing of Clostridium butyricum and Kiebsiella pneumoniae in gly- cerol fer-mentation. Biotechnology and Bioengineering, 1994, 44: 902-911.
[4] 修志龙, 曾安平, 安利佳. 甘油生物转化为1,3-丙二醇过程的动力学数学模拟和多稳态研究[J]. 大连理工大学学报, 2000, 44: 428-433.
[5] Y. Q. Sun, 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. Biochemical Engineering Journal, 2008, 38: 22-32.
[6] J. X. Ye, E. M. Feng, L. Wang, Z. L. Xiu and Y. Q. Sun. Model- ing and robustness analysis of biochemical networks of glyc-erol metabolism by Klebsiella pneumoniae. Complex Sciences Lec- ture Notes of the Institute for Computer Sciences, Social Inform- atics and Telecommunications Engineering, Springer, Berlin Heidelberg, 2009, 4: 446-457.
[7] J. Wang, J. X. Ye, E. M. Feng, H. C. Yin and B. Tan. Complex metabolic network of glycerol by Klebsiella pneumo-niae and its system identification via biological robustness. Nonlinear Ana- lysis: Hybrid Systems, 2011, 5(1): 102-112.
[8] J. Wang, J. X. Ye, E. M. Feng, H. C. Yin and Z. L. Xiu. Model- ling and identification of a nonlinear hybrid dynamical system in batch fermentation of glyc-erol. Mathematical and Computer Modelling, 2011, 54(1-2): 618-624.
[9] B. Y. Shen, C. Y. Liu, J. X. Ye, E. M. Feng and Z. L. Xiu. Para- meter identification and optimization algorithm in microbial continu-ous culture. Applied Mathematical Modelling, 2012, 36: 585-595.
[10] J. G. Zhai, J. X. Ye, L. Wang, E. M. Feng, H. C. Yin and Z. L. Xiu. Pathway identification using parallel optimization for a complex metabolic system in microbial continuous culture, Non- linear Analysis: Real World Applications, 2011, 12(5): 2730- 2741.
[11] J. Wang, J. X. Ye, H. C. Yin, E. M. Feng and L. Wang. Sensitiv- ity analysis and identification of kinetic parameters in batch fer- mentation of glycerol. Journal of Computational and Applied Mathematics, 2012, 236(9): 2268-2276.
[12] V. Rehbock, K. L. Teo and L. S. Jennings. A computational pro- cedure for suboptimal robust controls. Dynamics and Control, 1992, 2(4): 331-348.
[13] R. Loxton, K. L. Teo and V. Rehbock. Robust suboptimal control of nonlinear systems. Applied Mathematics and Computation, 2011, 217: 6566-6576.
[14] D. He, H. Ji and T. Zheng. On robustness of suboptimal min- max model predic-tive control. WSEAS Transactions on Systems and Control, 2007, 2: 428-433.
[15] 马知恩, 周义仓. 常微分方程定性与稳定性方法[M]. 北京: 科学出版社, 2009.
[16] J. Kennedy, R. Eberhart. Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, Perth: IEEE, 1995: 1942-1948.

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