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

Lei Wang

Abstract and Applied Analysis, 2012, vol. 2012, 1-15

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:295627

DOI: 10.1155/2012/295627

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