批式流加发酵中的鲁棒脉冲时滞最优控制  

Robust impulsive time-delay optimal control in fed-batchfermentation process

作　　者：宫召华[1] 时郭庆 GONG Zhaohua;SHI Guoqing(School of Mathematics and Information Science,Shandong Technology and Business University,Yantai,Shandong 264005;Yantai Haiyi Software Company Limited,Yantai,Shandong 264003)

机构地区：[1]山东工商学院数学与信息科学学院,山东烟台264005 [2]烟台海颐软件股份有限公司,山东烟台264003

出　　处：《石河子大学学报（自然科学版）》2024年第3期376-382,共7页Journal of Shihezi University(Natural Science)

基　　金：山东省自然科学基金项目(ZR2023MA054)。

摘　　要：本文研究了批式流加发酵中的鲁棒脉冲时滞最优控制问题。首先,提出一个非线性状态依赖的脉冲时滞系统描述批式流加发酵甘油生产1,3-丙二醇(1,3-PD)过程。由于批式流加发酵过程中的动力学参数难以准确估计,本文建立了一个具有连续状态不等式约束的鲁棒脉冲时滞最优控制模型。这里,目标函数为终端时刻1,3-PD浓度及其关于动力学参数的灵敏性的加权和,控制向量为流加发生时甘油的临界浓度及每次流加时甘油的流加体积。然后,通过引入辅助脉冲系统,将该鲁棒最优控制问题转化为等价的标准最优控制问题。进一步,通过约束转换技术,将等价的最优控制问题转化为仅具有盒式约束的罚问题。最后,设计了一种并行差分进化算法求解转化后的罚问题。数值结果表明:当参数受到微小扰动时,尽管牺牲了少量的1,3-PD浓度,但是明显提高了系统的鲁棒性。The robust impulsive time-delay optimal control problem in a fed-batch fermentation process is investigated.Firstly,we propose a nonlinear state-dependent impulsive time-delay system to describe the process of fermenting glycerol to produce 1,3-propanediol(1,3-PD)in fed-batch fermentation.Due to the difficulty in accurately estimating the kinetic parameters during the fed-batch fermentation process,a robust time-delay optimal control model subject to continuous state inequality constraints is proposed.Here,the objective function is the weighted sum of the terminal concentration of 1,3-PD and its sensitivity with respect to kinetic parameters,and the control vector includes the critical concentration of glycerol and the volume of adding glycerol at each feeding time in the feeding processes.Furthermore,by introducing an auxiliary impulsive system,the robust optimal control problem is transformed into an equivalent standard optimal control problem.By applying the constraint transcription technique,the equivalent optimal control problem is converted into a penalty problem with only box constraints.Finally,a parallel differential evolution algorithm is developed to solve the transformed penalty problem.The numerical results indicate that although a small amount of 1,3-PD concentration is sacrificed,the robustness of the system is significantly improved when the parameters are subjected to small disturbances.

关 键 词：非线性脉冲系统 最优控制 约束转换 差分进化算法 批式流加发酵 

分 类 号：O232[理学—运筹学与控制论]