Modeling and parameter estimation of a nonlinear switching system in fed-batch culture with pH feedback

In this paper, we propose a nonlinear switching system to formulate the coupled fed-batch culture with pH feedback of glycerol to 1,3-propanediol by Klebsiella pneumoniae and discuss its some basic properties. The parametric sensitivity functions are also given to obtain the derivatives of solutions with respect to the unknown kinetic parameters. To estimate those parameters from the experimental data, we present a parameter estimation problem with inequality path constraints. By constraint transcription and local smoothing technique, the estimation problem is transformed and solved by an optimization algorithm, which is constructed via sensitivity functions approach. Finally, an illustrative numerical example shows the appropriateness of the nonlinear switching system and the validity of optimization algorithm.