微生物批式流加发酵多阶段最优控制的最优性条件(英文)

Optimality Condition of Multistage Optimal Control for Microbial Fed-Batch Culture

在微生物批式流加发酵生产1,3-丙二醇(1,3-PD)过程中,关键是如何控制甘油和碱的流加速度.本文将流加速度看成一个随时间变化的控制函数,提出一个带控制的多阶段动力系统描述批式发酵过程,并证明了系统的一些性质.以终端时刻1,3-PD的生产强度最大为性能指标,以上述动力系统和连续状态不等式为约束条件建立了最优控制模型,最后利用不可微优化理论得到了最优控制问题的最优性条件,并证明了最优性条件和最优性函数零点的等价性.

In fed-batch culture of glycerol bio-dissimilation to 1,3-propanediol （1,3- PD）, proper feed rates of glycerol and alkali are required. In this paper, by taking the feed rate of glycerol as the control function, we propose a controlled multistage system to formulate the fed-batch culture process. Some properties of the system are also proved. Subsequently, we present an optimal control model subject to the above dynamical system and continuous state inequality constraints. Finally, we obtain an optimality condition for the optimal control problem by non-differentiable optimization theory, and prove the equivalence between the optimality condition and zeros of an optimality function.