批式流加与连续发酵的非光滑动力系统辨识与优化控制
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摘要
本文以甘油微生物歧化生产1,3—丙二醇的批式流加与连续发酵为背景,研究了一类非线性脉冲系统与非光滑非线性动力系统的辨识与最优控制问题.根据实际批式流加发酵过程的特点,建立了非线性状态依赖脉冲微分系统.考虑连续发酵过程中底物与目标产物的跨膜运输方式及中间代谢物对发酵过程的影响,建立了八维非光滑非线性动力系统.本文的主要工作概括如下：
1.将甘油批式流加发酵过程中碱和甘油的流加过程看作为一个状态依赖脉冲过程,建立了描述批式流加发酵过程的非线性状态依赖脉冲动力系统.证明了该系统的非齐诺(Non-Zeno)性及其解的存在性与唯一性,以及系统解关于初值与参数的连续依赖性.以实验测试数据和计算值之间的绝对误差作为性能指标建立了系统的参数辨识模型,证明了此参数辨识模型的可辨识性,并构造了改进的微粒群算法对参数辨识模型进行求解.数值结果表明所建立的非线性状态依赖脉冲系统能更好地描述该批式流加过程.
2.在批式流加发酵过程中,每次向发酵罐中流加多少碱和甘油是很关键的.本文以甘油的流加量作为控制变量,建立了描述批式流加发酵过程的非线性状态依赖脉冲控制系统,其脉冲时刻及脉冲时刻的状态跳跃幅度都是状态依赖的.以系统终端时刻目标产物浓度的最大化为性能指标,建立了带有连续状态不等式约束和控制约束的最优状态依赖脉冲控制模型,通过约束处理技术将最优状态依赖脉冲控制问题转化为一个等价的控制问题,并利用变分法推导出最优控制的最优性必要条件.
3.考虑胞内胞外两个代谢环境及甘油与1,3—丙二醇的物质被动扩散和细胞主动转运相结合的跨膜运输方式,同时考虑有毒的中间代谢物3-羟基丙醛对甘油脱水酶(GDHt)(?)口1,3—丙二醇氧化还原酶(PDOR)的活性的临界抑制作用及其对细胞生长的临界抑制作用,建立了描述甘油微生物歧化生产1,3—丙二醇的连续发酵过程的八维非光滑非线性动力系统,证明了该动力系统解的存在唯一性、解关于参数的连续性以及解集的紧性.以计算稳态值与实验获得的稳态数据的平均相对误差为性能指标,以多个非光滑非线性动力系统为约束,建立了参数辨识模型,证明了其可辨识性.构造了改进并行微粒群优化算法分别在底物限制和底物过量的条件下对该参数辨识模型进行求解.数值计算结果表明所建立的数学模型能很好的描述连续发酵过程,也表明了用并行微粒群优化算法求解该辨识模型是有效的.
This dissertation investigates the identification and optimal control of a class of nonlinear impulsive system and non-smooth nonlinear dynamical system in the process of bioconversion glycerol to1,3-propanediol. According to the characteristic of fed-batch culture, a nonlinear state-dependent impulsive system is established to formulate the process of the culture. In terms of the transports of substrate and product across cell membrane, and the effects of the interme-diate in the continuous culture process, we develop a non-smooth nonlinear eight-dimensional dynamical system to simulate and optimize the process. The main contributions of the disserta-tion are summarized as follows:
1. Taking the feeding process as a state-dependent impulses process, a nonlinear state-dependent impulsive system is proposed to formulate the process of fed-batch culture. The existence, uniqueness and regularity of solution to the system and continuous depen-dence of the solution on initial value and parameters are proved. Regarding the absolute error between the experimental results and calculated values as the performance index, a parameter identification model is presented. The identifiability of the parameter identifi-cation model is also proved. Finally, an improved particle swarm optimization algorithm is constructed to find the optimal parameters for the model. Numerical results show that the nonlinear state-dependent impulsive system can be used to describe the fed-batch culture better.
2. During the process of fed-batch culture, how much substrate to feed is important. In this dissertation, a nonlinear impulsive controlled system, in which the volume of feeding is the control variable and both jumps size of state and impulsive moments are state-dependent, is proposed to formulate the fed-batch fermentation process. To maximize the concentration of target product at the terminal time, an optimal control model involving the nonlinear state-dependent impulsive controlled system and subject to the continuous state inequality constraint and the control constraint is presented. In order to deduce the optimality conditions, the optimal control model is transcribed into an equivalent one by treating the constraints. Finally, the optimality conditions of the optimal control model are investigated by calculus of variations.
3. In this dissertation, an eight-dimensional non-smooth nonlinear dynamic system is devel-oped to formulate the continuous culture of bioconversion glycerol to1,3-PD, in which the passive diffusion and active transport of glycerol and1,3-PD across cell membrane, and3-hydroxypropionaldehyde inhibition to cells growth for its toxicity and to the ac-tivity of GDHt and PDOR when its concentration is higher than a certain value are all taken into consideration. Then, the existence, uniqueness, continuous dependence of the solution on the parameter vector and the compactness of solution set are all proved. Tak-ing the mean relative error between the experimental data and calculated values as the cost functional, a parameter identification model involving multiple eight-dimensional non-smooth nonlinear dynamic systems is presented. The identifiability of the parameter identification model is also proved. An improved parallel particle swarm optimization algorithm is constructed to find the optimal parameters for the systems under substrate limitation and excess conditions, respectively. Numerical results show that the nonlinear dynamic model can describe the fermentation process better and the algorithm is effective to solve the parameter identification model.
1.将甘油批式流加发酵过程中碱和甘油的流加过程看作为一个状态依赖脉冲过程,建立了描述批式流加发酵过程的非线性状态依赖脉冲动力系统.证明了该系统的非齐诺(Non-Zeno)性及其解的存在性与唯一性,以及系统解关于初值与参数的连续依赖性.以实验测试数据和计算值之间的绝对误差作为性能指标建立了系统的参数辨识模型,证明了此参数辨识模型的可辨识性,并构造了改进的微粒群算法对参数辨识模型进行求解.数值结果表明所建立的非线性状态依赖脉冲系统能更好地描述该批式流加过程.
2.在批式流加发酵过程中,每次向发酵罐中流加多少碱和甘油是很关键的.本文以甘油的流加量作为控制变量,建立了描述批式流加发酵过程的非线性状态依赖脉冲控制系统,其脉冲时刻及脉冲时刻的状态跳跃幅度都是状态依赖的.以系统终端时刻目标产物浓度的最大化为性能指标,建立了带有连续状态不等式约束和控制约束的最优状态依赖脉冲控制模型,通过约束处理技术将最优状态依赖脉冲控制问题转化为一个等价的控制问题,并利用变分法推导出最优控制的最优性必要条件.
3.考虑胞内胞外两个代谢环境及甘油与1,3—丙二醇的物质被动扩散和细胞主动转运相结合的跨膜运输方式,同时考虑有毒的中间代谢物3-羟基丙醛对甘油脱水酶(GDHt)(?)口1,3—丙二醇氧化还原酶(PDOR)的活性的临界抑制作用及其对细胞生长的临界抑制作用,建立了描述甘油微生物歧化生产1,3—丙二醇的连续发酵过程的八维非光滑非线性动力系统,证明了该动力系统解的存在唯一性、解关于参数的连续性以及解集的紧性.以计算稳态值与实验获得的稳态数据的平均相对误差为性能指标,以多个非光滑非线性动力系统为约束,建立了参数辨识模型,证明了其可辨识性.构造了改进并行微粒群优化算法分别在底物限制和底物过量的条件下对该参数辨识模型进行求解.数值计算结果表明所建立的数学模型能很好的描述连续发酵过程,也表明了用并行微粒群优化算法求解该辨识模型是有效的.
This dissertation investigates the identification and optimal control of a class of nonlinear impulsive system and non-smooth nonlinear dynamical system in the process of bioconversion glycerol to1,3-propanediol. According to the characteristic of fed-batch culture, a nonlinear state-dependent impulsive system is established to formulate the process of the culture. In terms of the transports of substrate and product across cell membrane, and the effects of the interme-diate in the continuous culture process, we develop a non-smooth nonlinear eight-dimensional dynamical system to simulate and optimize the process. The main contributions of the disserta-tion are summarized as follows:
1. Taking the feeding process as a state-dependent impulses process, a nonlinear state-dependent impulsive system is proposed to formulate the process of fed-batch culture. The existence, uniqueness and regularity of solution to the system and continuous depen-dence of the solution on initial value and parameters are proved. Regarding the absolute error between the experimental results and calculated values as the performance index, a parameter identification model is presented. The identifiability of the parameter identifi-cation model is also proved. Finally, an improved particle swarm optimization algorithm is constructed to find the optimal parameters for the model. Numerical results show that the nonlinear state-dependent impulsive system can be used to describe the fed-batch culture better.
2. During the process of fed-batch culture, how much substrate to feed is important. In this dissertation, a nonlinear impulsive controlled system, in which the volume of feeding is the control variable and both jumps size of state and impulsive moments are state-dependent, is proposed to formulate the fed-batch fermentation process. To maximize the concentration of target product at the terminal time, an optimal control model involving the nonlinear state-dependent impulsive controlled system and subject to the continuous state inequality constraint and the control constraint is presented. In order to deduce the optimality conditions, the optimal control model is transcribed into an equivalent one by treating the constraints. Finally, the optimality conditions of the optimal control model are investigated by calculus of variations.
3. In this dissertation, an eight-dimensional non-smooth nonlinear dynamic system is devel-oped to formulate the continuous culture of bioconversion glycerol to1,3-PD, in which the passive diffusion and active transport of glycerol and1,3-PD across cell membrane, and3-hydroxypropionaldehyde inhibition to cells growth for its toxicity and to the ac-tivity of GDHt and PDOR when its concentration is higher than a certain value are all taken into consideration. Then, the existence, uniqueness, continuous dependence of the solution on the parameter vector and the compactness of solution set are all proved. Tak-ing the mean relative error between the experimental data and calculated values as the cost functional, a parameter identification model involving multiple eight-dimensional non-smooth nonlinear dynamic systems is presented. The identifiability of the parameter identification model is also proved. An improved parallel particle swarm optimization algorithm is constructed to find the optimal parameters for the systems under substrate limitation and excess conditions, respectively. Numerical results show that the nonlinear dynamic model can describe the fermentation process better and the algorithm is effective to solve the parameter identification model.
引文
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