A stochastic model for microbial fermentation process under Gaussian white noise environment

Abstract

In this paper, we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis, where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises. In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model. Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values.

Optimal control of a batch fermentation process with nonlinear time-delay and free terminal time and cost sensitivity constraint

“…Clearly, it is computationally expensive to solve the new problem, defined on the new time horizon. Thus, another way is needed to get the value of x(s delay |x 01 , x 02 , T, σ) and then solve (21).…”

“…The different identification problems for nonlinear hybrid dynamical system in batch fermentation are investigated in [19,20]. A stochastic model for microbial fermentation process under Gaussian white noise environment is considered in [21]. Joint estimation of batch fermentation is carried out by using unscented kalman filter in [22].…”

Robust optimization for nonlinear time-delay dynamical system of dha regulon with cost sensitivity constraint in batch culture

“…A nonlinear dynamical system involving concentration changes of three intracellular substances and two key enzymes is proposed in [10]. Based on these mathematical models, batch culture has become a hot research topic, including suboptimal control problems [11], robust optimal control problems [12], multi-stage system [13,14,15], sensitivity analysis [16], robust identification problems [17], pathway identification problems [18], stochastic model [19] joint estimation [20] and hybrid system [21].…”