一类微生物发酵的非线性混杂动力系统辨识及控制
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摘要
本文以微生物间歇发酵和批式流加发酵生产1,3-丙二醇为背景,研究了一类非线性混杂动力系统与非线性脉冲动力系统的建模、辨识和最优控制.另外,针对代谢物质跨膜运输机理的生物专家知识,研究了基于模糊专家知识的混合动力系统及参数辨识.这项研究不仅丰富了混杂系统、参数辨识、优化算法和不确定性建模等理论与数值计算方法,而且对提高终端产物的产量提供参考.因此,对该领域的研究具有一定的理论价值和实际应用价值.本文研究的工作可以概括为：
1.针对一类脉冲流加形式的耦合批式流加发酵非线性脉冲动力系统,提出了最大化目标产物的最优控制模型,其中以底物甘油和碱液的流加体积和流加时刻为优化变量.依系统解集的紧性,证明了最优控制模型解的存在性.通过引入新的时间尺度函数,得到等价的最优控制问题.然后,根据约束转换和光滑近似技术,提出了基于梯度的优化算法.经数值计算,获得了最优流加体积和最优流加时刻的耦合批式流加发酵策略.
2.提出了非线性混杂动力系统来描述带有开环控制和逻辑反馈控制的非耦合的批式流加发酵过程.证明了系统的性质和系统解的适定性.为了确定系统参数,建立了带有混杂动力系统为约束的参数辨识模型.根据灵敏度函数和光滑函数,给出了约束泛函和成本泛函关于参数的一阶偏导数.最后构造了一个基于梯度搜索方向的优化算法.数值计算结果表明提出的混杂动力系统的合理性,及本文给出的优化算法的可行性.
3.依模糊系统表达生物专家知识,并与酶催化动力系统相结合构造了描述甘油间歇发酵过程的非线性混合动力系统.证明了系统的主要性质.为了估计系统参数和模糊系统的隶属度函数,提出了一个带有混合系统和连续状态不等式约束的辨识模型,并证明了该辨识模型的可辨识性.基于改进的粒子群优化算法和罚函数法,构造了一个优化算法.数值计算结果表明了提出的混合系统不仅能描述甘油间歇发酵过程而且还能反映出甘油发酵过程中的专家知识.
This dissertation is based on the background of microbial production of1,3-Propanediol in the batch and fed-batch fermentation of glycerol by Klebsiella pneumoniae. This dissertation studies the modelling, system identification and optimization of this class fed-batch fermen-tation process. Additionally, based on qualitative heuristic knowledge from biochemists, the hybrid system modelling and identification of batch fermentation by using fuzzy system ap-proach is also studied. The research can not only develop nonlinear hybrid dynamical system, optimal control theory, optimization algorithm and the modeling method of unascertain system but also provide certain reference for commercial process of1,3-Propanediol by fermentation. Therefore, it is very interesting both in theory and in practice. The main contributions are summarized as follows:
1. Considering the fed-batch fermentation process of glycerol coupled alkali, a nonlinear impulsive dynamical system is proposed to formulate this process. To obtain as much1,3-Propanediol as possible, an optimal control model involving the proposed impulsive system and subject to continuous state inequality constraints is then presented, in which impulsive instants and volumes of feeding glycerol and alkali are taken as control vari-ables. Subsequently the existence of the optimal control is proved. A solution approach is developed to seek the optimal impulsive strategies of glycerol and alkali based on gra-dient information. By numerical calculation, the optimal impulsive strategy of glycerol and alkali then are obtained.
2. In this dissertation, a nonlinear hybrid dynamical system is proposed to formulate the fed-batch fermentation of glycerol by Klebsiella pneumoniae with open loop glycerol input and pH logic control. Some important properties of the solution to the proposed system are then discussed, including the existence, uniqueness, boundedness and regularity. To estimation the unknown parameters in the system, a parameter identification problem is proposed, and its identifiability is also proved. Subsequently, the parametric sensitivity functions of the system are given and utilized to obtain the requisite gradient information for further numerical computation. Finally a gradient-based algorithm to solve the identi-fication problem is constructed in conjunction with constraint transcription and smoothing approximation technique. Numerical simulations show the proposed hybrid system can describe the fed-batch culture properly.
3. In this dissertation, a novel model for describing the process of glycerol batch fermenta-tion is proposed by incorporating qualitative heuristic knowledge from biochemists via a fuzzy expert system approach into Enzyme-catalysis dynamical system. Some important properties of the proposed system are then discussed. To determine the model parameters and membership functions, we establish a parameter identification model with the relative error of experimental data and simulating results as performance index, and demonstrate the existence of the optimal solutions of the identification model. An optimization algo-rithm is developed to solve the identification model based on improved particle swarm optimization and penalty function method. Finally, the numerical simulations show the validity of the proposed model and the effectiveness of the optimization algorithm.
1.针对一类脉冲流加形式的耦合批式流加发酵非线性脉冲动力系统,提出了最大化目标产物的最优控制模型,其中以底物甘油和碱液的流加体积和流加时刻为优化变量.依系统解集的紧性,证明了最优控制模型解的存在性.通过引入新的时间尺度函数,得到等价的最优控制问题.然后,根据约束转换和光滑近似技术,提出了基于梯度的优化算法.经数值计算,获得了最优流加体积和最优流加时刻的耦合批式流加发酵策略.
2.提出了非线性混杂动力系统来描述带有开环控制和逻辑反馈控制的非耦合的批式流加发酵过程.证明了系统的性质和系统解的适定性.为了确定系统参数,建立了带有混杂动力系统为约束的参数辨识模型.根据灵敏度函数和光滑函数,给出了约束泛函和成本泛函关于参数的一阶偏导数.最后构造了一个基于梯度搜索方向的优化算法.数值计算结果表明提出的混杂动力系统的合理性,及本文给出的优化算法的可行性.
3.依模糊系统表达生物专家知识,并与酶催化动力系统相结合构造了描述甘油间歇发酵过程的非线性混合动力系统.证明了系统的主要性质.为了估计系统参数和模糊系统的隶属度函数,提出了一个带有混合系统和连续状态不等式约束的辨识模型,并证明了该辨识模型的可辨识性.基于改进的粒子群优化算法和罚函数法,构造了一个优化算法.数值计算结果表明了提出的混合系统不仅能描述甘油间歇发酵过程而且还能反映出甘油发酵过程中的专家知识.
This dissertation is based on the background of microbial production of1,3-Propanediol in the batch and fed-batch fermentation of glycerol by Klebsiella pneumoniae. This dissertation studies the modelling, system identification and optimization of this class fed-batch fermen-tation process. Additionally, based on qualitative heuristic knowledge from biochemists, the hybrid system modelling and identification of batch fermentation by using fuzzy system ap-proach is also studied. The research can not only develop nonlinear hybrid dynamical system, optimal control theory, optimization algorithm and the modeling method of unascertain system but also provide certain reference for commercial process of1,3-Propanediol by fermentation. Therefore, it is very interesting both in theory and in practice. The main contributions are summarized as follows:
1. Considering the fed-batch fermentation process of glycerol coupled alkali, a nonlinear impulsive dynamical system is proposed to formulate this process. To obtain as much1,3-Propanediol as possible, an optimal control model involving the proposed impulsive system and subject to continuous state inequality constraints is then presented, in which impulsive instants and volumes of feeding glycerol and alkali are taken as control vari-ables. Subsequently the existence of the optimal control is proved. A solution approach is developed to seek the optimal impulsive strategies of glycerol and alkali based on gra-dient information. By numerical calculation, the optimal impulsive strategy of glycerol and alkali then are obtained.
2. In this dissertation, a nonlinear hybrid dynamical system is proposed to formulate the fed-batch fermentation of glycerol by Klebsiella pneumoniae with open loop glycerol input and pH logic control. Some important properties of the solution to the proposed system are then discussed, including the existence, uniqueness, boundedness and regularity. To estimation the unknown parameters in the system, a parameter identification problem is proposed, and its identifiability is also proved. Subsequently, the parametric sensitivity functions of the system are given and utilized to obtain the requisite gradient information for further numerical computation. Finally a gradient-based algorithm to solve the identi-fication problem is constructed in conjunction with constraint transcription and smoothing approximation technique. Numerical simulations show the proposed hybrid system can describe the fed-batch culture properly.
3. In this dissertation, a novel model for describing the process of glycerol batch fermenta-tion is proposed by incorporating qualitative heuristic knowledge from biochemists via a fuzzy expert system approach into Enzyme-catalysis dynamical system. Some important properties of the proposed system are then discussed. To determine the model parameters and membership functions, we establish a parameter identification model with the relative error of experimental data and simulating results as performance index, and demonstrate the existence of the optimal solutions of the identification model. An optimization algo-rithm is developed to solve the identification model based on improved particle swarm optimization and penalty function method. Finally, the numerical simulations show the validity of the proposed model and the effectiveness of the optimization algorithm.
引文
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