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

本CAREER提案提出了对一类新的控制问题的基本研究，即集成控制，它涉及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获和实验单个原子，成像大脑，以及生成生物大分子的结构和动态信息。从这些新兴技术中产生的许多应用涉及到通过使用相同的控制场来控制一个大的量子系综，例如，在阿伏伽德罗数（6X1023）的数量级上。在许多情况下，集合的元素表现出表征系统动力学特性的参数值的变化。例如，在磁共振实验中，一个系综的核自旋在其固有频率中可能具有色散，因此系综的自旋在其固有频率中可能具有色散，因此具有不同激励（脉冲序列）的自旋可以将具有不同动力学的系综从初始状态引导到期望的最终状态。面临的挑战是同时控制具有相同控制信号的兴趣点之间的连续系统。我们计划为这种欠驱动系统提供可控性条件和最优控制技术。由此产生的方法，通过对集成控制问题的系统研究，可以直接应用于核磁共振（NMR）光谱和成像（MRI）中最佳脉冲序列的设计。拟议的工作将促进统计？数学控制理论的最先进的方法和广泛的应用，包括医学成像，结构生物学，以及量子信息处理。PI不仅建议充分利用上述生物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。拟议的职业规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，致力于解决现实世界的问题。例如，学生将为MRI系统设计最佳脉冲序列，并将其应用于真实的MRI机器上。

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.