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STABILITY AND OPTIMAL CONTROL OF MICROORGANISMS IN CONTINUOUS CULTURE
Li, Xiaohong,Feng, Enmin,Xiu, Zhilong 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1
The process of producing 1,3-preprandiol by microorganism continuous cultivation would attain its equilibrium state. How to get the highest concentration of 1,3-propanediol at that time is the aim for producers. Based on this fact, an optimization model is introduced in this paper, existence of optimal solution is proved. By infinite-dimensional optimal theory, the optimal condition of model is given and the equivalence between optimal condition and the zero of optimality function is proved.
Li, Kezan,Feng, Enmin,Xiu, Zhilong 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
According to the controllability of pulse times and the amount of jumps in the states at these times in the process of fed-batch culture producing 1,3-propanediol, this paper proposes a terminal optimal control model, whose constraint condition is the nonlinear impulsive delay system. The existence of optimal control is discussed and an optimization algorithm which is applied to each subinternal over one cycle for this optimal control problem is constructed. Finally, the numerical simulations show that the terminal intensity of producing 1,3-propanediol has been increased obviously.
Stability and optimal control of microorganisms in continuous culture
Xiaohong Li,Enmin Feng,Zhilong Xiu 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1-2
The process of producing 1,3-preprandiol by microorganism continuous cultivation would attain its equilibrium state. How to get the highest concentration of 1,3-propanediol at that time is the aim for producers. Based on this fact, an optimization model is introduced in this paper, existence of optimal solution is proved. By infinite-dimensional optimal theory, the optimal condition of model is given and the equivalence between optimal condition and the zero of optimality function is proved.
Nonlinear impulsive system of microbial production in fed-batch culture and its optimal control
Caixia Gao,Yanhuai Lang,Enmin Feng,Zhilong Xiu 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1-2
In this study the optimal control of fed-batch glycerol fermentation is investigated based on an impulsive dynamical system. Considering the sudden increase of the glycerol and alkali in fed-batch culture of biodissimilation of glycerol to 1,3- propanediol, this paper proposes a nonlinear impulsive system of fed-batch culture. The existence, uniqueness and regularity properties of piecewise solution for the system are proved. In view of the controllability of volumes of glycerol added to the reactor instantaneously, the paper constructs an optimal control model based on the nonlinear impulsive system and the existence of the optimal control is obtained. The control variables here are the moments and the sizes of jumps in the states at the discrete instants and the objective is to maximize the productivity of 1,3-propanediol over one cycle.
NONLINEAR IMPULSIVE SYSTEM OF MICROBIAL PRODUCTION IN FED-BATCH CULTURE AND ITS OPTIMAL CONTROL
GAO, CAIXIA,LANG, YANHUAI,FENG, ENMIN,XIU, ZHILONG 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1
In this study the optimal control of fed-batch glycerol fermentation is investigated based on an impulsive dynamical system. Considering the sudden increase of the glycerol and alkali in fed-batch culture of biodissimilation of glycerol to 1,3-propanediol, this paper proposes a non-linear impulsive system of fed-batch culture. The existence, uniqueness and regularity properties of piecewise solution for the system are proved. In view of the controllability of volumes of glycerol added to the reactor instantaneously, the paper constructs an optimal control model based on the nonlinear impulsive system and the existence of the optimal control is obtained. The control variables here are the moments and the sizes of jumps in the states at the discrete instants and the objective is to maximize the productivity of 1,3-propanediol over one cycle.