Modelling and optimal control for an impulsive dynamical system in microbial fed-batch culture

In this paper, we consider modelling and optimal control of a microbial fed-batch culture. A nonlinear impulsive dynamical system with variable impulsive instants and volumes of feeding glycerol and alkali is proposed to formulate the fed-batch culture of 1,3-propanediol (1,3-PD). To obtain as much 1,3-PD as possible, an optimal control model involving the proposed impulsive system and subject to continuous state inequality constraints is then presented, in which the 1,3-PD concentration at the terminal moment is taken as the cost function, and impulsive instants and volumes of feeding glycerol and alkali are taken as control variables. Subsequently, the existence of the optimal control is proved. A solution approach is developed to seek the optimal impulsive strategies of glycerol and alkali based on constraint transcription and smoothing approximation techniques. Numerical results show the concentration of 1,3-PD at the terminal moment is indeed increased considerably by employing the optimal impulsive strategy.

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