一类非线性切换系统的多目标优化理论与算法

项目名称： 一类非线性切换系统的多目标优化理论与算法

项目编号： No.11201267

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 刘重阳

作者单位： 山东工商学院

项目金额： 23万元

中文摘要： 切换系统和多目标优化理论与算法以其重要的理论价值和广泛的应用背景一直是研究的热点。本项目以微生物发酵甘油生产1,3-丙二醇为研究背景对一类非线性切换系统的多目标优化理论与算法展开研究。首先，针对生化过程中存在某些代谢机理不清和过程多阶段的特性，建立非线性切换系统，该系统具有高度非线性、分片光滑和系统切换等特点。研究该系统的一些重要性质。其次，依生化过程中测得的部分数据和生物系统的鲁棒性，建立多目标系统辨识模型；以目标产物产量最大、原料消耗最小和时间消耗最短等作为性能指标，建立多目标最优切换控制模型。最后，对于多目标系统辨识问题和多目标最优控制问题，将应用变分分析、多目标优化、不可微优化、组合优化和半无限优化等研究这类优化问题的有效解集或弱有效解集的性质、最优性条件和优化算法。该项研究不仅可以推动切换系统、多目标优化理论和优化算法的研究，还可以实现生化过程的优化和控制，创造可观的经济效益。

中文关键词： 不可微优化；多目标最优控制；多目标系统辨识；半无限优化；切换系统

英文摘要： The research about switched systems and theory and algorithm of multiobjective optimization is always a focus due to their valuable theory and wide applications. This project develops the research of multiobjective optimization theory and algorithm for a class of nonlinear switched systems derived from microbial fermentation process of glycerol to 1,3-propanediol. In this project, a class of nonlinear switched systems is firstly proposed to describe the unclarity of some metabolic mechanisms and multistage characteristics in the fermentation process. The systems are of high nonlinearity, piecewise smoothness and system switching properties. Furthermore, some important properties are discussed. Taking the experimental data and the robustness of the biological system as the cost function, a multiobjective system identification model is then presented. In addition, to maximize the target product, minimize the consumed material and minimize the fermentation time, a multiobjective optimal switching control model is investigated. Finally, for the multiobjective optimization problems, some theories such as variational analysis, multiobjective optimization, nondifferential optimization, combinatorial optimization and semi-infinite optimization will be applied to discussing the properties of efficient or weak efficient s

英文关键词： Nodifferentiable optimization；multi-objective optimal control；multi-objective system identification；semi-infinite optimization；switched system