Modelling and parameter identification for a two-stage fractional dynamical system in microbial batch process
Articles
Chongyang Liu
Shandong Technology and Business University
https://orcid.org/0000-0002-2229-6717
Xiaopeng Yi
Shandong Technology and Business University
https://orcid.org/0000-0001-6468-3486
Yanli Feng
Shandong Technology and Business University
Published 2022-03-01
https://doi.org/10.15388/namc.2022.27.26234
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Keywords

fractional dynamical system
parameter identification
parallel optimization
batch fermentation

How to Cite

Liu, C., Yi, X. and Feng, Y. (2022) “Modelling and parameter identification for a two-stage fractional dynamical system in microbial batch process”, Nonlinear Analysis: Modelling and Control, 27(2), pp. 350–367. doi:10.15388/namc.2022.27.26234.

Abstract

In this paper, we consider mathematical modelling and parameter identification problem in bioconversion of glycerol to 1,3-propanediol by Klebsiella pneumoniae. In view of the dynamic behavior with memory and heredity and experimental results in batch culture, a two-stage fractional dynamical system with unknown fractional orders and unknown kinetic parameters is proposed to describe the fermentation process. For this system, some important properties of the solution are discussed. Then, taking the weighted least-squares error between the computational values and the experimental data as the performance index, a parameter identification model subject to continuous state inequality constraints is presented. An exact penalty method is introduced to transform the parameter identification problem into the one only with box constraints. On this basis, we develop a parallel Particle Swarm Optimization algorithm to find the optimal fractional orders and kinetic parameters. Finally, numerical results show that the model can reasonably describe the batch fermentation process, as well as the effectiveness of the developed algorithm. Keywords: fractional dynamical system, parameter identification, parallel optimization,

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