Computational Methods in Laser Molecular Control and Parameter Estimation

研究人员将在圣巴巴拉的加州大学控制工程和计算中心（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。 拟议的工作强调数学和工程之间的积极互动，理论和应用之间。 研究者将发起并与CCEC成员合作开展跨学科研究项目。 特别是，他将与CCEC研究主任Dahleh教授在分子系统控制领域合作。 基于分子系统的量子模型，他们试图回答这样的问题：是否可能有一定的化学反应速率，如果可能，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的现实分子系统的可控性评估。 沿着的还有CCEC的一名成员Alasasekaran教授，他还将为估计和滤波问题开发快速有效的算法。 估计中的一个关键问题涉及所使用的不确定性模型。 如果不确定性模型没有给出问题中真实不确定性的准确表示，而是超出了它，那么它将导致性能不佳的过度保守的结果。 研究人员和教授martrasekaran将明确包括结构化数据的不确定性到最小二乘类型的估计问题。 结构不确定性的例子是位移结构（Toeplitz，Hankel等）。和块结构的不确定性。 位移结构出现在存在LTI（线性时不变）系统的地方。 块结构更常见，并且在存在子系统时会出现。 研究员将应用新获得的工程和应用数学专业知识来监督数学和工程专业的跨学科高级项目，并将数学更好地融入工程课程。 该IGMS项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）共同支持。

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).