Vector measure for explicit nonlinear impulsive system of glycerol bioconversion in fed-batch cultures and its parameter identification

In this paper, the nonlinear dynamical system of fed-batch fermentation is investigated in the process of bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae. Taking into account the abrupt changes of concentrations of glycerol and the priority of the value of state to the jump in fed-batch culture, we propose a explicit nonlinear impulsive dynamical system of glycerol bioconversion to 1,3-propanediol driven by a vector-valued measure in fed-batch fermentation, which is fit for the factual fermentation better than continuous models in being. We study the existence and uniqueness of solutions to the impulsive system. Because of errors between experimental results and numerical simulation results of the proposed impulsive system, we establish the parameter identification model for the impulsive system and discuss the identifiability of the parameters and continuous dependence on parameters. Finally in order to find the optimal parameters of the impulsive system, a hybrid particle swarm optimization algorithm is constructed. Numerical results of simulations show that the optimization algorithm is valid.