Journal of Optimization Theory and Applications

, Volume 167, Issue 1, pp 342–362 | Cite as

Robust Optimal Control of a Microbial Batch Culture Process



This paper considers the microbial batch culture process for producing 1,3-propanediol (1,3-PD) via glycerol fermentation. Our goal was to design an optimal control scheme for this process, with the aim of balancing two (perhaps competing) objectives: (i) the process should yield a sufficiently high concentration of 1,3-PD at the terminal time and (ii) the process should be robust with respect to changes in various uncertain system parameters. Accordingly, we pose an optimal control problem, in which both process yield and process sensitivity are considered in the objective function. The control variables in this problem are the terminal time of the batch culture process and the initial concentrations of biomass and glycerol in the batch reactor. By performing a time-scaling transformation and introducing an auxiliary dynamic system to calculate process sensitivity, we obtain an equivalent optimal control problem in standard form. We then develop a particle swarm optimization algorithm for solving this equivalent problem. Finally, we explore the trade-off between process efficiency and process robustness via numerical simulations.


Nonlinear dynamic system Microbial batch culture Robust control System sensitivity 

Mathematics Subject Classification

34H05 49M25 49M37 93C41 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11171050, 11101262, and 11371164) and the National Natural Science Foundation for the Youth of China (Grant Nos. 11301081, 11401073).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Guanming Cheng
    • 1
  • Lei Wang
    • 1
  • Ryan Loxton
    • 2
    • 3
  • Qun Lin
    • 2
  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Department of Mathematics and StatisticsCurtin UniversityPerthAustralia
  3. 3.Institute of Cyber-Systems and ControlZhejiang UniversityHangzhouPeople’s Republic of China

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