US-Turkey Cooperative Research: Semi-Analytical Treatments of Nonlinear Stochastic Dynamical Systems with Application to Control Problems

美国-土耳其合作研究：非线性随机动力系统的半解析处理及其在控制问题中的应用

• 批准号: 0217453
• 负责人: Jian-Qiao Sun
• 金额: $ 3.44万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0217453&HistoricalAwards=false
• 关键词: US; Turkey; Cooperative; Research; Semi

0217453SunDescription: This award is for support of a joint research project by Dr. Jian-Qiao Sun, Department of Mechanical Engineering at the University of Delaware, Newark, Delaware and Dr. Ghazanfer Unal, Engineering Science Department at Istanbul Technical University, Istanbul, Turkey. The goal of this project is to develop analytical and numerical methods to study the stochastic dynamical systems. The investigators plan to extend Lie's theory for deterministic differential equations to nonlinear stochastic dynamical systems. Specifically, they will extend their previous results on the approximate symmetries to stochastic dynamical systems in a manner which will remain consistent with the normal form theory of stochastic systems. An immediate use of the approximate symmetries of the stochastic dynamical systems would be to obtain their approximate conserved quantities. Furthermore, they will extend the results to the Fokker-Planck equation in order to obtain analytical approximate solutions. The analytical solutions to be obtained in the project by Professor Unal will be integrated with the cell mapping method studied by Dr. Sun. The approximate symmetries and the related conservation laws can help identify a sub-space in which the cell mapping method can be applied. This is expected to substantially reduce the computational effort for analysis and control of nonlinear stochastic systems by using the cell mapping method.Scope:Success in determining approximate symmetries and the related conservation laws would make it possible to identify a subspace in which cell mapping can be applied with much less resources than currently possible. The two scientists have complementary strengths, as Dr. Sun's expertise is in cell mapping, while Dr. Unal's expertise is in Lie's theory and in symmetries and approximate symmetries of dynamical systems. Research results will be integrated with graduate programs at both universities, and an exchange program of graduate students between the two universities may also result. Dr. Unal will travel to the United States in the first and third years while Prof. Sun will travel to Turkey in the second year. The project will lead to long-term collaboration between them since they will tackle difficult problems that require new insights, as well as advanced computational tools.

0217453 Sun描述：该奖项是为了支持特拉华州大学机械工程系的Jian-Qiao Sun博士和土耳其伊斯坦布尔技术大学工程科学系的Ghazanfer Unal博士的联合研究项目。 本计画的目标是发展分析与数值方法来研究随机动力系统。 研究人员计划将李的确定性微分方程理论扩展到非线性随机动力系统。具体来说，他们将以与随机系统的规范形理论保持一致的方式将之前关于近似对称性的结果扩展到随机动力系统。 随机动力系统的近似对称性的一个直接应用是获得它们的近似守恒量。 此外，他们将结果推广到福克-普朗克方程，以获得解析近似解。Unal教授在该项目中获得的解析解将与孙博士研究的细胞映射方法相结合。 近似对称性和相关的守恒律可以帮助确定可以应用胞映射方法的子空间。预计这将大大减少使用胞映射方法分析和控制非线性随机系统的计算量。范围：成功确定近似对称性和相关守恒律将使识别一个子空间成为可能，在该子空间中可以应用胞映射，而所需资源比目前可能的要少得多。这两位科学家具有互补的优势，因为Sun博士的专长是细胞映射，而Unal博士的专长是Lie理论和动力系统的对称性和近似对称性。 研究成果将与两所大学的研究生课程相结合，两所大学之间的研究生交流计划也可能产生。 Unal博士将在第一年和第三年前往美国，而Sun教授将在第二年前往土耳其。 该项目将导致他们之间的长期合作，因为他们将解决需要新的见解以及先进的计算工具的难题。