Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach

doi:10.1016/j.cjche.2021.03.041

Chinese Journal of Chemical Engineering ›› 2022, Vol. 44 ›› Issue (4): 192-204.DOI: 10.1016/j.cjche.2021.03.041

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Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach

Xiang Wu^1,3, Yuzhou Hou², Kanjian Zhang^4,5, Ming Cheng³

1 School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China;
2 School of Life Sciences, Guizhou Normal University, Guiyang 550001, China;
3 School of Electrical Engineering, Southeast University, Nanjing 210096, China;
4 School of Automation, Southeast University, Nanjing 210096, China;
5 Key Laboratory of Measurement and Control of CSE, Ministry of Education, Southeast University, Nanjing 210096, China

Received:2020-12-03 Revised:2021-02-27 Online:2022-06-18 Published:2022-04-28
Contact: Xiang Wu,E-mail:xwu@seu.edu.cn;Yuzhou Hou,E-mail:yuzhou_hou@163.com
Supported by:
This work was supposed by the National Natural Science Foundation of China (61963010 and 61563011), and the special project for cultivation of new academic talent and innovation exploration of Guizhou Normal University in 2019 (11904-0520077).

Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach

Xiang Wu^1,3, Yuzhou Hou², Kanjian Zhang^4,5, Ming Cheng³

1 School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China;
2 School of Life Sciences, Guizhou Normal University, Guiyang 550001, China;
3 School of Electrical Engineering, Southeast University, Nanjing 210096, China;
4 School of Automation, Southeast University, Nanjing 210096, China;
5 Key Laboratory of Measurement and Control of CSE, Ministry of Education, Southeast University, Nanjing 210096, China

通讯作者: Xiang Wu,E-mail:xwu@seu.edu.cn;Yuzhou Hou,E-mail:yuzhou_hou@163.com
基金资助:
This work was supposed by the National Natural Science Foundation of China (61963010 and 61563011), and the special project for cultivation of new academic talent and innovation exploration of Guizhou Normal University in 2019 (11904-0520077).

Abstract

Abstract: This paper considers a dynamic optimization problem (DOP) of 1,3-propanediol fermentation process (1,3-PFP). Our main contributions are as follows. Firstly, the DOP of 1,3-PFP is modeled as an optimal control problem of switched dynamical systems. Unlike the existing switched dynamical system optimal control problem, the state-dependent switching method is applied to design the switching rule. Then, in order to obtain the numerical solution, by introducing a discrete-valued function and using a relaxation technique, this problem is transformed into a nonlinear parameter optimization problem (NPOP). Although the gradient-based algorithm is very efficient for solving NPOPs, the existing algorithm is always trapped in a local minimum for such problems with multiple local minima. Next, in order to overcome this challenge, a gradient-based random search algorithm (GRSA) is proposed based on an improved gradient-based algorithm (IGA) and a novel random search algorithm (NRSA), which cannot usually be trapped in a local minimum. The convergence results are also established, and show that the GRSA is globally convergent. Finally, a DOP of 1,3-PFP is provided to illustrate the effectiveness of the GRSA proposed by this paper.

Key words: Process control, Optimization, Mathematical modeling, Switched system, State-dependent switching, Global optimization

摘要： This paper considers a dynamic optimization problem (DOP) of 1,3-propanediol fermentation process (1,3-PFP). Our main contributions are as follows. Firstly, the DOP of 1,3-PFP is modeled as an optimal control problem of switched dynamical systems. Unlike the existing switched dynamical system optimal control problem, the state-dependent switching method is applied to design the switching rule. Then, in order to obtain the numerical solution, by introducing a discrete-valued function and using a relaxation technique, this problem is transformed into a nonlinear parameter optimization problem (NPOP). Although the gradient-based algorithm is very efficient for solving NPOPs, the existing algorithm is always trapped in a local minimum for such problems with multiple local minima. Next, in order to overcome this challenge, a gradient-based random search algorithm (GRSA) is proposed based on an improved gradient-based algorithm (IGA) and a novel random search algorithm (NRSA), which cannot usually be trapped in a local minimum. The convergence results are also established, and show that the GRSA is globally convergent. Finally, a DOP of 1,3-PFP is provided to illustrate the effectiveness of the GRSA proposed by this paper.

关键词: Process control, Optimization, Mathematical modeling, Switched system, State-dependent switching, Global optimization

Xiang Wu, Yuzhou Hou, Kanjian Zhang, Ming Cheng. Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach[J]. Chinese Journal of Chemical Engineering, 2022, 44(4): 192-204.

Xiang Wu, Yuzhou Hou, Kanjian Zhang, Ming Cheng. Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach[J]. 中国化学工程学报, 2022, 44(4): 192-204.

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Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach

Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach

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