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2015, 5(1): 59-69. doi: 10.3934/naco.2015.5.59

## Optimal dilution strategy for a microbial continuous culture based on the biological robustness

 1 School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, China, China 2 School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350108, China

Received  January 2015 Revised  March 2015 Published  March 2015

A robust optimal parameter selection model is proposed to formulate the microbial continuous culture process of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD), in which the dilution rate and the glycerol concentration in feed medium are taken as the optimization variables. In consideration of the uncertain factors that some system parameters may be changed with the change of the optimization variables, we establish a novelty mathematical model which is represented by an eight-dimensional nonlinear dynamical system with the unknown parameters. On the basis of biological robustness, we give a quantitative definition of robustness index. The concentration of 1,3-PD at the approximately steady-state time together with the robustness index are taken as the cost functional in consideration of uncertain metabolic mechanisms. A parallel particle swarm optimization -- optimal parameter selection algorithm (PPSO-OPSA) is constructed to find the optimal dilution rate and the feeding glycerol concentration. Numerical results show that, by employing the obtained optimal input strategy, not only the concentration of 1,3-PD at the approximately steady-state time can be increased considerably compared with the previous experimental results, but also the obtained optimal parameters are robust for the dynamical system.
Citation: Jingang Zhai, Guangmao Jiang, Jianxiong Ye. Optimal dilution strategy for a microbial continuous culture based on the biological robustness. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 59-69. doi: 10.3934/naco.2015.5.59
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##### References:
 [1] Lei Wang, Jinlong Yuan, Yingfang Li, Enmin Feng, Zhilong Xiu. Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness. Numerical Algebra, Control & Optimization, 2014, 4 (2) : 103-113. doi: 10.3934/naco.2014.4.103 [2] Jinggui Gao, Xiaoyan Zhao, Jinggang Zhai. Optimal control of microbial fed-batch culture involving multiple feeds. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 339-349. doi: 10.3934/naco.2015.5.339 [3] Qi Yang, Lei Wang, Enmin Feng, Hongchao Yin, Zhilong Xiu. Identification and robustness analysis of nonlinear hybrid dynamical system of genetic regulation in continuous culture. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2018168 [4] Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin. Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture. Journal of Industrial & Management Optimization, 2009, 5 (4) : 835-850. doi: 10.3934/jimo.2009.5.835 [5] K. Schittkowski. Optimal parameter selection in support vector machines. Journal of Industrial & Management Optimization, 2005, 1 (4) : 465-476. doi: 10.3934/jimo.2005.1.465 [6] Ka Wo Lau, Yue Kuen Kwok. Optimal execution strategy of liquidation. Journal of Industrial & Management Optimization, 2006, 2 (2) : 135-144. doi: 10.3934/jimo.2006.2.135 [7] Yanan Mao, Caixia Gao, Ruidong Yan, Aruna Bai. Modeling and identification of hybrid dynamic system in microbial continuous fermentation. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 359-368. doi: 10.3934/naco.2015.5.359 [8] Ross Callister, Duc-Son Pham, Mihai Lazarescu. Using distribution analysis for parameter selection in repstream. Mathematical Foundations of Computing, 2019, 2 (3) : 215-250. doi: 10.3934/mfc.2019015 [9] Andrea Arnold, Daniela Calvetti, Erkki Somersalo. Vectorized and parallel particle filter SMC parameter estimation for stiff ODEs. Conference Publications, 2015, 2015 (special) : 75-84. doi: 10.3934/proc.2015.0075 [10] Fengjun Wang, Qingling Zhang, Bin Li, Wanquan Liu. Optimal investment strategy on advertisement in duopoly. Journal of Industrial & Management Optimization, 2016, 12 (2) : 625-636. doi: 10.3934/jimo.2016.12.625 [11] Hanqing Jin, Xun Yu Zhou. Continuous-time portfolio selection under ambiguity. Mathematical Control & Related Fields, 2015, 5 (3) : 475-488. doi: 10.3934/mcrf.2015.5.475 [12] Vinicius Albani, Adriano De Cezaro, Jorge P. Zubelli. On the choice of the Tikhonov regularization parameter and the discretization level: A discrepancy-based strategy. Inverse Problems & Imaging, 2016, 10 (1) : 1-25. doi: 10.3934/ipi.2016.10.1 [13] R. S. Johnson. A selection of nonlinear problems in water waves, analysed by perturbation-parameter techniques. Communications on Pure & Applied Analysis, 2012, 11 (4) : 1497-1522. doi: 10.3934/cpaa.2012.11.1497 [14] Glenn Ledder, Donna Sylvester, Rachelle R. Bouchat, Johann A. Thiel. Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy. Mathematical Biosciences & Engineering, 2018, 15 (4) : 841-862. doi: 10.3934/mbe.2018038 [15] Guibin Lu, Qiying Hu, Youying Zhou, Wuyi Yue. Optimal execution strategy with an endogenously determined sales period. Journal of Industrial & Management Optimization, 2005, 1 (3) : 289-304. doi: 10.3934/jimo.2005.1.289 [16] Heinz Schättler, Urszula Ledzewicz, Benjamin Cardwell. Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis. Mathematical Biosciences & Engineering, 2011, 8 (2) : 355-369. doi: 10.3934/mbe.2011.8.355 [17] Bangyu Shen, Xiaojing Wang, Chongyang Liu. Nonlinear state-dependent impulsive system in fed-batch culture and its optimal control. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 369-380. doi: 10.3934/naco.2015.5.369 [18] Giselle A. Monteiro, Milan Tvrdý. Generalized linear differential equations in a Banach space: Continuous dependence on a parameter. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 283-303. doi: 10.3934/dcds.2013.33.283 [19] Honghan Bei, Lei Wang, Yanping Ma, Jing Sun, Liwei Zhang. A linear optimal feedback control for producing 1, 3-propanediol via microbial fermentation. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020095 [20] A. Zeblah, Y. Massim, S. Hadjeri, A. Benaissa, H. Hamdaoui. Optimization for series-parallel continuous power systems with buffers under reliability constraints using ant colony. Journal of Industrial & Management Optimization, 2006, 2 (4) : 467-479. doi: 10.3934/jimo.2006.2.467

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