Optimal control for nonlinear dynamical system of microbial fed-batch culture

In fed-batch culture of glycerol bio-dissimilation to 1, 3-propanediol (1, 3-PD), the aim of adding glycerol is to obtain as much 1, 3-PD as possible. So a proper feeding rate is required during the process. Taking the concentration of 1, 3-PD at the terminal time as the performance index and the fe...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 232; no. 2; pp. 252 - 261
Main Author: Liu, Chongyang
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 15.10.2009
Elsevier
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Fed-batch culture
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Nonlinear dynamical system
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Optimal control
Parametrization method
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Parametrization method
Nonlinear dynamical system
Fed-batch culture
37N25
Optimal control
49J15
Optimization method
Optimal policy
State space
Non linear programming
Dynamical system
Parameterization
Penalty method
Convergence
State constraint
Mathematical programming
Approximation
Control system
Nonlinear problems
State space method
Non linear system
Constrained optimization
Numerical analysis
Applied mathematics
Non linear model
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:In fed-batch culture of glycerol bio-dissimilation to 1, 3-propanediol (1, 3-PD), the aim of adding glycerol is to obtain as much 1, 3-PD as possible. So a proper feeding rate is required during the process. Taking the concentration of 1, 3-PD at the terminal time as the performance index and the feeding rate of glycerol as the control function, we propose an optimal control model subject to a nonlinear dynamical system and constraints of continuous state and non-stationary control. A computational approach is constructed to seek the solution of the above model in two aspects. On the one hand we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space; on the other hand, 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 of this approximation is also investigated. Numerical results show that, by employing the optimal control policy, the concentration of 1, 3-PD at the terminal time can be increased considerably.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2009.06.006