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2011 Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture
Lei Wang, Zhilong Xiu, Yuduo Zhang, Enmin Feng
J. Appl. Math. 2011: 1-11 (2011). DOI: 10.1155/2011/624516


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.


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Lei Wang. Zhilong Xiu. Yuduo Zhang. Enmin Feng. "Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture." J. Appl. Math. 2011 1 - 11, 2011.


Published: 2011
First available in Project Euclid: 15 March 2012

zbMATH: 1227.92026
MathSciNet: MR2820076
Digital Object Identifier: 10.1155/2011/624516

Rights: Copyright © 2011 Hindawi


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