Journal of Applied Mathematics

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

Lei Wang, Zhilong Xiu, Yuduo Zhang, and Enmin Feng

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 624516, 11 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331818613

Digital Object Identifier
doi:10.1155/2011/624516

Mathematical Reviews number (MathSciNet)
MR2820076

Zentralblatt MATH identifier
1227.92026

Citation

Wang, Lei; Xiu, Zhilong; Zhang, Yuduo; Feng, Enmin. Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture. J. Appl. Math. 2011 (2011), Article ID 624516, 11 pages. doi:10.1155/2011/624516. https://projecteuclid.org/euclid.jam/1331818613


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