微生物批式流加发酵过程中的时滞最优控制

Time-delay optimal control problem in microbial fed-batch fermentation process

考虑到1, 3-丙二醇(1, 3-PD)批式流加发酵过程中的时滞现象,提出一个非线性时滞微分方程来描述该过程.以终端时刻1, 3-PD的单位时间产量作为性能指标,同时,以甘油和碱的流加速度、发酵过程的终端时刻作为控制向量,建立一个含控制和状态约束的时滞最优控制模型.为了求解该最优控制问题,首先通过时间尺度变换,将该最优控制问题转化为具有固定终端时刻的等价最优控制问题;然后,应用控制参数化方法,将等价的最优控制问题用一系列有限维优化问题来近似;最后,构造一种改进的粒子群优化方法来求解相应的近似优化问题.数值结果表明,终端时刻的1, 3-PD的单位时间产量比已有结果提高了约58%.

Considering the time-delay in fermentation process, we propose a nonlinear time-delay system to describe the fed-batch process of glycerol bioconversion to 1, 3-propanediol(1, 3-PD). Taking the 1, 3-PD yield of per unit time at the terminal time as the performance index, regarding the feeding rates of glycerol and 1, 3-PD as well as the terminal time as the control variables, we present a time-delay optimal control problem subject to control and state constraints. To solve this optimal control problem, by using time-scaling transformation, we first transform it into an equivalent one with fixed terminal time. Then, the equivalent problem is approximated by a sequence of finite-dimensional optimization problems using the control parameterization method. Finally, an improved particle swarm optimization method is constructed to solve the approximate optimization problem. Numerical results show that 1, 3-PD yield of per unit time at the terminal time increases 58% compared with the previous result.