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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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 |
work_keys_str_mv |
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