Modeling and parameter identification for a nonlinear multi-stage system for dha regulon in batch culture

Abstract

The bioconversion of glycerol to 1,3-propanediol (1,3-PD) is a complex bioprocess. In this paper, based on biological phenomena of different characteristics at different stages and the genetic regulation of dha regulon, we consider a fourteen-dimensional nonlinear multi-stage dynamic system with unknown time and system parameters for formulating the multi-stage cell growth in batch culture. Some important properties of the multi-stage system are discussed. Our goal is to identify the time and system parameters. To this end, we present a parameter identification problem in which the time and system parameters are decision variables and the cost function measures the discrepancy between experimental data and computational results, subject to the multi-stage system, parameter constraints and continuous state inequality constraints. The system sensitivity (the cost function’s gradient, namely, the derivative of the cost function with respect to the time and system parameters), which can be computed by solving an auxiliary initial value problem, can be regarded as the search direction of optimization algorithm. The identification problem is converted into a sequence of nonlinear programming subproblems through the application of the time-scaling transformation, the constraint transcription and local smoothing approximate techniques. Due to the highly complex nature of the identification problem, the computational cost is high. Thus, a parallel algorithm is proposed to solve these subproblems based on the novel combinations of system sensitivity and genetic algorithm. Finally, numerical results show that the multi-stage system can reasonably describe the process of batch culture.