CAREER: Ensemble Control with Applications to Spectroscopy, Imaging, and Computation

职业：系综控制及其在光谱学、成像和计算中的应用

• 批准号: 0747877
• 负责人: Jr-Shin Li
• 金额: $ 40万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0747877&HistoricalAwards=false
• 关键词: CAREER; Ensemble; Control; Applications; Spectroscopy

This CAREER proposal proposes a fundamental investigation of a new class of control problems, Ensemble Control, which involves controlling a large number of dynamical systems with the same control signal. State-of-the-art quantum technology can trap and experiment with individual atoms, image brains as well as generate structural and dynamical information of biological macromolecules. Numerous applications arising from such emerging techniques involve controlling a large quantum ensemble, e.g., on the order of Avogadro number (6X1023), by use of the same control field. In many cases, the elements of the ensemble show variations in the values of the parameters characterizing the system dynamics. For example, in magnetic resonance experiments, nuclear spins of an ensemble may have a dispersion in their natural frequencies, so that the spins of an ensemble may have a dispersion in their natural frequencies, so that spins with different excitations (pulse sequences) that can steer such an ensemble of systems with different dynamics from an initial state of desired final state. The challenge is to simultaneously steer a continuum of systems between points of interest with the same control signal. We plan to provide controllability conditions and optimal control techniques for such under-actuated systems. The resulting methodology, via a systematic study of ensemble control problems, can be directly applied to the design of optimal pulse sequences in Nuclear Magnetic Resonance (NMR) spectroscopy and imaging (MRI). The proposed work will advance stat-of ?the-art methods of mathematical control theory and has broad applications including medical imaging, structural biology, as well as quantum information processing. The PI proposes not only to make best use of engineering expertise in above areas of biology and quantum mechanics, but also to help make methods and problems in these fields more accessible to engineers. The proposed CAREER plan provides educational activities and research opportunities for both undergraduates and graduate students to work on multidisciplinary projects. They will work in close collaboration with scientists in other disciplines and will work on solving real world problems. For example, students will design optimal pulse sequences for MRI systems and will implement them onto the real MRI machines.

这份职业计划提出了对一类新的控制问题的基础研究，集合控制涉及到用相同的控制信号控制大量的动态系统。最先进的量子技术可以捕捉和实验单个原子，成像大脑，以及产生生物大分子的结构和动力学信息。这种新兴技术产生的许多应用涉及通过使用相同的控制场来控制大的量子系综，例如，在阿伏加德罗数(6X1023)的数量级上。在许多情况下，系综元素表现出表征系统动力学的参数值的变化。例如，在磁共振实验中，系综核自旋在其自然频率中可能具有色散，从而系综的自旋可能在其自然频率中具有色散，从而具有不同激励(脉冲序列)的自旋可以从所需的最终状态的初始状态引导具有不同动力学的这样的系统的系综。挑战在于用相同的控制信号同时在关注点之间操纵系统的连续体。我们计划为这类欠驱动系统提供可控性条件和最优控制技术。通过对系综控制问题的系统研究，所得到的方法可以直接应用于核磁共振(核磁共振)谱和成像(MRI)中的最佳脉冲序列的设计。所提出的工作将推进数学控制理论的最先进方法，并具有广泛的应用，包括医学成像、结构生物学以及量子信息处理。PI不仅建议最大限度地利用上述生物学和量子力学领域的工程专业知识，而且还建议帮助工程师更容易获得这些领域的方法和问题。拟议的职业计划为本科生和研究生提供了从事多学科项目的教育活动和研究机会。他们将与其他学科的科学家密切合作，并致力于解决现实世界的问题。例如，学生将为核磁共振系统设计最佳脉冲序列，并将其应用到真实的核磁共振机器上。