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Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture

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  • Lei Wang

Abstract

A hybrid system with state-based switchings is proposed to describe the fed-batch production of 1,3-propandiol from glycerol in our previous work. However, the on-off switching of alkali is too frequent, which greatly increases the computational cost of the numerical solution to the system so as to locate the state-based switchings in strict time order and implement the correct mode changes. To deal with this problem, we consider the switching of alkali pump as an impulsive event and present a nonlinear impulsive switching system to describe the fed-batch culture. It is proved that the impulsive switching system is non-Zeno. Some basic properties of solutions to the impulsive switching system are also explored. In order to overcome the discontinuities of the system, the Skorohod topology is induced and a specific form of λ is constructed to prove the main theorem. Additionally, a numerical simulation is carried out to show that the proposed system can describe the fed-batch culture properly and the essential difference with the previous work.

Suggested Citation

  • Lei Wang, 2012. "Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, March.
  • Handle: RePEc:hin:jnlaaa:295627
    DOI: 10.1155/2012/295627
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    Cited by:

    1. Yuan, Jinlong & Zhu, Xi & Zhang, Xu & Yin, Hongchao & Feng, Enmin & Xiu, Zhilong, 2014. "Robust identification of enzymatic nonlinear dynamical systems for 1,3-propanediol transport mechanisms in microbial batch culture," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 150-163.

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