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Operations Research Transactions >

2025 , Vol. 29 >Issue 4: 219 - 230

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.04.017

Research Article

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

  • Jia WANG ,
  • Yuzhi HUANG ,
  • Jianxiong YE
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  • 1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, Fujian, China
    2. College of Computer and Cyber Security, Fujian Normal University, Fuzhou 350117, Fujian, China

Received date: 2022-11-01

  Online published: 2025-12-11

Copyright

, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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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

Cite this article

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

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