Modelling and optimization for a switched system in microbial fed-batch culture

This paper considers modelling and optimization of a microbial fed-batch fermentation process. A switched system with variable switching instants is proposed to describe the fermentation process of glycerol bioconversion to 1,3-propanediol (1,3-PD). Taking the concentration of 1,3-PD at the terminal time as the cost function and the switching instants as optimization variables, an optimization model involving switched system and subject to continuous state inequality constraints is then presented. By introducing a time-scaling transform, the optimization model is transcribed into an equivalent one with parameters and fixed switching instants. A computational approach to seek the optimal solution is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that, by employing the optimal switching instants, the concentration of 1,3-PD can be increased considerably compared with previous results.