Nonlinear state-dependent impulsive system and its parameter identification in microbial fed-batch culture

In fed-batch culture of glycerol to 1,3-propanediol by Klebsiella pneumoniae, glycerol and alkali are fed in batches into the bioreactor to provide sufficient nutrition and maintain a suitable environment for cells growth. In this paper, taking the feeding process as a state-dependent impulses process, a nonlinear state-dependent impulsive system is proposed to formulate the fed-batch process. Some important properties of the solution to the system are discussed, i.e., the existence, uniqueness and regularity of solution to the system and continuous dependence of the solution on initial value and parameters. Regarding the errors between the experimental results and calculated values as the performance index, a parameter identification model is presented. The identifiability of the parameter identification model is also proved. Finally, an improved particle swarm optimization (PSO) algorithm is constructed to seek the optimal parameters. Numerical results show that the nonlinear state-dependent impulsive system can be used to describe the fed-batch culture reasonably .