Modeling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol. (English) Zbl 1225.37110
Summary: A nonlinear hybrid dynamical system is established to describe the batch culture of glycerol to \(1,3\)-propanediol (\(1,3\)-PD) by Klebsiella pneumoniae (K. pneumoniae), in which glycerol is assumed to pass the cell membrane by passive diffusion coupled with facilitated transport and transport mechanism of \(1,3\)-PD is assumed to be uncertain. The existence, uniqueness and continuity of solutions are also discussed. To infer the most reasonable transport mechanism of \(1,3\)-PD, a system identification model consisting of both discrete and continuous variables is proposed. Additionally, we construct a two-phase optimization algorithm on the basis of modified complex method together with very fast simulated annealing technology. Numerical results show that it is most reasonable for \(1,3\)-PD to pass the cell membrane by passive diffusion coupled with facilitated transport and that the optimization algorithm is valid.
MSC:
| 37N25 | Dynamical systems in biology |
| 92C40 | Biochemistry, molecular biology |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 90C90 | Applications of mathematical programming |
| 93A30 | Mathematical modelling of systems (MSC2010) |
| 93B30 | System identification |
Keywords:
batch culture; transport mechanisms; nonlinear hybrid dynamical system; system identification; optimization algorithmReferences:
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