Computational Methods in Laser Molecular Control and Parameter Estimation

激光分子控制和参数估计的计算方法

• 批准号: 0075127
• 负责人: Caixing Gu
• 金额: $ 9.74万
• 依托单位: California Polytechnic State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2002-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0075127&HistoricalAwards=false
• 关键词: Computational; Methods; Laser; Molecular; Control

The investigator will spend a year at the Center for Control Engineering and Computation (CCEC) of the University of California at Santa Barbara. This will allow him to obtain a sound foundation in the fields of control systems and signal processing and apply this knowledge in his subsequent research. The proposed work emphasizes the positive interactions between mathematics and engineering, and between theory and application. The investigator will initiate and collaborate on interdisciplinary research projects with members of the CCEC. In particular, he will work with Professor Dahleh, the research director at the CCEC, in the area of control of molecular systems. Based on the quantum models of the molecular systems they seek to answer the question of whether a certain chemical reaction rate is possible, and if so what sort of control input is needed. This work will involve the determination of efficient computational algorithms for the assessment of controllability of realistic molecular systems. Along with Professor Chandrasekaran, also a member of the CCEC, the investigator will also develop fast and efficient algorithms for estimation and filtering problems. A critical issue in estimation concerns the uncertainty model used. If the uncertainty model does not give an accurate representation of the true uncertainty in the problem but rather overbounds it, then it will lead to overly conservative results with poor performance. The investigator and Professor Chandrasekaran will explicitly include structured data uncertainties into least-squares type estimation problems. Examples of structured uncertainties are displacement-structured (Toeplitz, Hankel and etc.) and block-structured uncertainties. Displacement structures arise where there are LTI (linear time-invariant) systems. Block structures are more common and will occur when there are sub-systems. The investigator will apply the newly acquired expertise in engineering and applied mathematics to supervise interdisciplinary senior projects for both mathematics and engineering majors and to better integrate mathematics into the engineering curriculum. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).

研究者将在加州大学圣巴巴拉分校的控制工程与计算中心（CCEC）工作一年。这将使他在控制系统和信号处理领域获得良好的基础，并将这些知识应用于他随后的研究中。提出的工作强调数学与工程、理论与应用之间的积极互动。该研究员将与CCEC成员发起并合作开展跨学科研究项目。特别是，他将与CCEC的研究主任Dahleh教授在分子系统控制领域进行合作。基于分子系统的量子模型，他们试图回答这样的问题：某种化学反应速率是否可能，如果可能的话，需要什么样的控制输入。这项工作将涉及确定有效的计算算法，以评估现实分子系统的可控性。与同样是CCEC成员的Chandrasekaran教授一起，研究者还将为估计和过滤问题开发快速有效的算法。评估中的一个关键问题是所使用的不确定性模型。如果不确定性模型不能准确表示问题的真实不确定性，而是超出了不确定性，则会导致结果过于保守，性能不佳。研究者和Chandrasekaran教授将明确地将结构化数据不确定性纳入最小二乘型估计问题。结构不确定性的例子有位移结构（Toeplitz， Hankel等）和块结构不确定性。位移结构出现在线性时不变系统中。块结构更常见，当有子系统时就会出现。该研究员将运用新获得的工程和应用数学专业知识来指导数学和工程专业的跨学科高级项目，并更好地将数学融入工程课程。该IGMS项目由MPS多学科活动办公室（OMA）和数学科学司（DMS）联合支持。