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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.
ZHANG, XU,LANG, YANHUAI,FENG, ENMIN 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.20 No.1
This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn't change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.
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.