Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture

In batch culture of glycerol biodissimilation to 1,3-propanediol (1,3-PD), the aim of adding glycerol is to obtain as much 1,3-PD as possible. Taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol, and terminal time as the control vector, we...

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Main Authors: Lei Wang, Zhilong Xiu, Yuduo Zhang, Enmin Feng
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2011/624516
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spelling doaj-cc342a0ee45b48009857dca20df2f41d2020-11-24T20:55:12ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/624516624516Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch CultureLei Wang0Zhilong Xiu1Yuduo Zhang2Enmin Feng3School of Life Science and Biotechnology, Dalian University of Technology, Dalian, Liaoning 116012, ChinaSchool of Life Science and Biotechnology, Dalian University of Technology, Dalian, Liaoning 116012, ChinaSchool of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, ChinaSchool of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, ChinaIn batch culture of glycerol biodissimilation to 1,3-propanediol (1,3-PD), the aim of adding glycerol is to obtain as much 1,3-PD as possible. Taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol, and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state. A computational approach is constructed to seek the solution of the above model. Firstly, we transform the optimal control problem into the one with fixed terminal time. Secondly, we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space. Finally, by approximating the control function with simple functions, we transform the unconstrained optimal control problem into a sequence of nonlinear programming problems, which can be solved using gradient-based optimization techniques. The convergence analysis and optimality function of the algorithm are also investigated. Numerical results show that, by employing the optimal control, the concentration of 1,3-PD at the terminal time can be increased, compared with the previous results.http://dx.doi.org/10.1155/2011/624516
collection DOAJ
language English
format Article
sources DOAJ
author Lei Wang
Zhilong Xiu
Yuduo Zhang
Enmin Feng
spellingShingle Lei Wang
Zhilong Xiu
Yuduo Zhang
Enmin Feng
Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
Journal of Applied Mathematics
author_facet Lei Wang
Zhilong Xiu
Yuduo Zhang
Enmin Feng
author_sort Lei Wang
title Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
title_short Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
title_full Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
title_fullStr Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
title_full_unstemmed Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
title_sort optimal control for multistage nonlinear dynamic system of microbial bioconversion in batch culture
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2011-01-01
description In batch culture of glycerol biodissimilation to 1,3-propanediol (1,3-PD), the aim of adding glycerol is to obtain as much 1,3-PD as possible. Taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol, and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state. A computational approach is constructed to seek the solution of the above model. Firstly, we transform the optimal control problem into the one with fixed terminal time. Secondly, we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space. Finally, by approximating the control function with simple functions, we transform the unconstrained optimal control problem into a sequence of nonlinear programming problems, which can be solved using gradient-based optimization techniques. The convergence analysis and optimality function of the algorithm are also investigated. Numerical results show that, by employing the optimal control, the concentration of 1,3-PD at the terminal time can be increased, compared with the previous results.
url http://dx.doi.org/10.1155/2011/624516
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