Vector measure as controls for explicit nonlinear impulsive system of fed-batch culture

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:351

Article

Wang, Gang¹  Feng, Enmin¹  Xiu, Zhilong² 

[1] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Liaoning, Peoples R China

[2] Dalian Univ Technol, Dept Biotechnol, Dalian 116024, Liaoning, Peoples R China

关键词: Bioconversion;    Fed-batch culture;    Explicit nonlinear impulsive dynamical system;    Vector measure;    Optimal control;   

DOI  :  10.1016/j.jmaa.2008.09.054

来源: Elsevier

【 摘 要 】

In this paper, we consider an optimal control problem of microbial fermentation process in which glycerol is converted to 1,3-propanediol by Klebsiella pneumoniae in fed-batch culture. During the period of reaction, the variation of pH Value is monitored to determine glycerol replenishment quantity, guaranteeing that microorganism can always keep growing fast under enough nutrition. Every time pH value is lower than seven, the quantity of glycerol added is Such that pH value returns seven again. Glycerol is poured into reactor at discrete time instant and the quantity is controllable. The problem is to determine for each discrete time instant the glycerol quantity to add and maximize the final concentration of 1,3-propanediol. We present a controlled explicit nonlinear impulsive dynamical system of fed-batch culture with state independent vector measures as controls and study the existence, uniqueness, boundedness, Continuous dependence and Gateaux differentiability Of its Solution with respect to controls. We then propose a Multiple objective programming model and demonstrate the regularity of cost functionals and weak compactness of admissible control set. Finally we discuss the existence of optimal control and implement a hybrid particle swarm optimization algorithm to solve the model optimally. Computational results are presented on a numerical example. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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