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Indexed by:期刊论文

Date of Publication:2013-01-01

Journal:NONLINEAR ANALYSIS-MODELLING AND CONTROL

Included Journals:SCIE、Scopus

Volume:18

Issue:1

Page Number:99-111

ISSN No.:1392-5113

Key Words:nonlinear stochastic system; stochastic optimal control; stochastic simulation; batch culture; bioconversion

Abstract:In this paper, we analyze a stochastic model representing batch fermentation in the process of glycerol bio-dissimilation to 1,3-propanediol by klebsiella pneumoniae. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Thus, based on the nonlinear deterministic dynamical system of glycerol bioconversion to 1,3-propanediol in batch culture, we present the stochastic version of the batch fermentation process driven by a five-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness and Markov property of solutions. Moveover a stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. Finally we present computer simulation for the stochastic system by using Stochastic Euler-Maruyama scheme. Compared with the results from the deterministic system, numerical results reveal the peculiar role of stochasticity in the dynamical responses of the batch culture.