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Practical algorithm for stochastic optimal control problem about microbial fermentation in batch culture

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Abstract

How to add glycerol to maximize production of 1,3-propanediol (1,3-PD) is a critical problem in process control of microbial fermentation. Most of the existing works are focusing on modelling this process through deterministic-based differential equations. However, this process is not deterministic, but intrinsically stochastic considering nature of interference. Thus, it is of importance to consider stochastic microorganism. In this paper, we will modelling this process through stochastic differential equations and maximizing production of 1,3-PD is formulated as an optimal control problem subject to continuous state constraints and stochastic disturbances. A modified particle swarm algorithm through integrating the hybrid Monte Carlo sampling and path integral is proposed to solve this problem. The constraint transcription, local smoothing and time-scaling transformation are introduced to handle the continuous state constraints. Numerical results show that, by employing the obtained optimal control governed by stochastic dynamical system, 1,3-PD concentration at the terminal time can be increased compared with the previous results.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants Nos. 11371164, 11771008 and 61473326), the National Natural Science Foundation for the Youth of China (Grants Nos. 11401073 and 11501574), the Fundamental Research Funds for Central Universities in China and the Natural Science Foundation of Shandong Province in China (Grant Nos. ZR2015FM014, ZR2015AL010 and ZR2017MA005).

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, Liaoning, People’s Republic of China

    Lei Wang & Jinlong Yuan

  2. Department of Mathematics, School of Science, Dalian Maritime University, Dalian, 116026, Liaoning, People’s Republic of China

    Jinlong Yuan

  3. Australasian Joint Research Centre for Building Information Modelling, School of Built Environment, Curtin University, Perth, 6845, Australia

    Changzhi Wu & Xiangyu Wang

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  1. Lei Wang
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  2. Jinlong Yuan
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  3. Changzhi Wu
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  4. Xiangyu Wang
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Correspondence to Changzhi Wu.

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Wang, L., Yuan, J., Wu, C. et al. Practical algorithm for stochastic optimal control problem about microbial fermentation in batch culture. Optim Lett 13, 527–541 (2019). https://doi.org/10.1007/s11590-017-1220-z

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