基于时间尺度变换的一类微生物批式流加发酵混杂切换系统的最优控制

doi:10.15960/j.cnki.issn.1007-6093.2025.04.017

Abstract

Abstract:

This paper considers the process control of the microbial production of 1,3-propanediol in fed-culture. This microbial process is in essential described as a hybrid switching system in which both autonomous switchings and controlled switchings are involved. By using time-scaling transformation, the controlled switching times are transformed to a sequence of integer time points in the new time horizon, resulting in a system composed of subsystems with autonomous switchings. Then, taking the feeding instants and the terminal time as control variables, we formulate an optimal control model with the productivity of 1,3-propanediol as performance index. The continuous state inequality constraints in the model are handled by the constraint transformation technique. A competitive particle swarm algorithm is constructed to solve the proposed optimal control problem and the optimal control strategies under different length of controlled subperiods are discussed. Numerical results show that, even if the number of switchings is reduced, it is still possible to achieve a relatively high productivity of 1,3-propanediol by sophisticated setting of the length of glycerol feeding time.

Key words: optimal control, hybrid switching system, time-scaling transformation, competitive particle swarm algorithm

CLC Number:

O232

Jia WANG, Yuzhi HUANG, Jianxiong YE. Optimal control of a hybrid switching system in a class of microbial fed-batch culture via time-scaling transformation[J]. Operations Research Transactions, 2025, 29(4): 219-230.

Figures/Tables 11

References 21

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参数	临界值	参数	临界值	参数	临界值	参数	临界值
$ d_s $	0.02	$ Y_2 $	0.013 133 4	$ {\rm pH}^* $	6.6	$ x_{2*} $	0
$ m_2 $	0	$ Y_3 $	97.785 9	$ x_1^* $	10	$ x_{3*} $	0
$ m_3 $	$ -2.670 \;3 $	$ Y_4 $	15.383 4	$ x_2^* $	2 039	$ x_{4*} $	0
$ m_4 $	0.002 921 45	$ Y_5 $	10.733 1	$ x_3^* $	1 370	$ x_{5*} $	0
$ m_5 $	0.040 800 5	$ \Delta_2 $	12.013 9	$ x_4^* $	1 026	$ x_{6*} $	0
$ K_2^* $	105.592	$ \Delta_3 $	7.559 7	$ x_5^* $	360.96	$ x_{7*} $	2
$ K_3^* $	99.793 1	$ \Delta_4 $	0.010 352	$ x_6^* $	500
$ K_4^* $	104.997	$ \Delta_5 $	0.102 197	$ x_7^* $	5
$ K_5^* $	90.622 6	$ {\rm pH}_* $	6.4	$ x_{1*} $	0

粒子数	$ x_3/t $的平均最优值	标准差
105	43.919 1	0.057 8

$ \delta/s $	粒子数	$ x_3/t $的最优值
100	105	43.965 0
200	105	44.180 5
300	105	44.271 8
400	105	44.272 5
1 800	105	44.341 6
3 600	105	44.327 4

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Optimal control of a hybrid switching system in a class of microbial fed-batch culture via time-scaling transformation

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