Targeted Coordination of Dynamic Populations: Fundamentals, Computational Methods, and Emerging Applications

在自然界和人类社会中，由孤立或相互作用的动态成分组成的复杂系统是普遍存在的。这类系统的典型例子包括大脑中的神经回路、生物学中的代谢化学反应系统、工程中的电力分配和交通控制系统。因此，解决控制和估计任务不仅针对一个动态系统，而且针对大量几乎相同的动态单元的整个种群，已成为许多科学和工程领域反复出现的主题，而精确定向协调和估计动态种群的能力将打开闸门，在各种前沿应用中取得快速而重大的进展。处理动态种群的根本困难在于，控制和观察只能在种群水平上实施，即，通过向种群中的所有系统广播单一输入信号，以及通过分别接收种群中系统的汇总测量，而且对于这类新的种群系统，基本上缺乏原则性的控制和观察策略。因此，以人口为基础的技术仍远未充分发挥其潜力。本研究旨在为各种新兴应用建立一个普遍和连贯的理论和计算框架，这些应用严重依赖于大量动态系统的有针对性的协调，从而缩小目前与人口系统有关的新兴应用问题的理论与实践之间的差距。拟议的调查将承诺对系统理论，控制工程，生物医学和量子技术做出新的贡献，并将反过来加强这些学科的研究和教育基础设施。将共同努力吸引代表性不足的群体和妇女参与研究项目，并通过华盛顿大学学校伙伴关系研究所（Institute for School Partnerships at Washington University）让公立学校和K-12预科学生参与科学研究。该项目将系统地调查有关广播信号的可控性的基本问题，以及关于人口中系统的综合测量的可观察性，并制定最佳控制策略，使人口中的动态结构能够有针对性地协调。通过将形式系统理论，集成控制技术，应用代数和几何与计算工程相结合，将制定人口控制的一般和通用框架。具体来说，控制分析和设计将通过利用与不同领域的高度不明显但基本密切的联系来进行，包括可控性的多项式近似和可观察性的数学断层扫描。对这些新联系的探索将拓宽理论和计算工作的范围，以理解复杂人口系统和网络的机制和集体行为。此外，所开发的理论和计算方法将应用于分析和控制群体系统的动态行为，包括诱导同步模式，解码复杂网络中的时空信息，揭示癌细胞信号网络中异质反应的驱动机制。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Complex systems that consist of populations of isolated or interacting dynamical components are prevalent in nature and human society. Notable examples of such systems include neural circuitry in the brain, metabolic chemical reaction systems in biology, and electrical power distribution, and traffic control systems in engineering. Tackling control and estimation tasks not only for one dynamical system but a whole population of a vast number of nearly identical dynamical units has thus emerged as a recurrent theme in numerous scientific and engineering areas, and the capability of precise targeted coordination and estimation of dynamic populations would open the floodgate to rapid and significant advancements in a diverse array of cutting-edge applications. The fundamental difficulty in dealing with dynamic populations is that control and observation can only be implemented at the population level, i.e., through broadcasting a single input signal to all the systems in the population, and through receiving aggregated measurements of the systems in the population, respectively, and there is a substantial lack of principled control and observation strategies for this new class of population systems. As a result, population-based technologies remain far from reaching their full potential. This research aims to establish a general and coherent theoretical and computational framework for the various emerging applications that critically rely on a targeted coordination of large populations of dynamical systems, and thereby close the current gap between theory and practice in the emerging applied problems concerned with population systems. The proposed investigation will promise new contributions to systems theory, control engineering, and biomedical and quantum technologies, and will in turn enhance the infrastructure for research and education across these disciplines. Concerted effort will be made to attract underrepresented groups and women to the research program and to engage the public and pre-college K-12 students in scientific research through the Institute for School Partnerships at Washington University.This project will systematically investigate fundamental questions of controllability with respect to a broadcast signal, as well as observability with respect to aggregated measurements of the systems in the population and develop optimal control strategies that will enable a targeted coordination of dynamical structures in populations. By bridging formal systems theory, ensemble control techniques, applied algebra and geometry with computational engineering, general and versatile frameworks for population control will be formulated. Specifically, the control analyses and designs will be carried through by leveraging highly non-obvious yet fundamentally intimate links to different domains, including polynomial approximation for controllability and mathematical tomography for observability. The exploration of these novel connections will broaden the range of the theoretical and computational efforts for understanding the mechanisms and collective behavior of complex population systems and networks. Moreover, the developed theoretical and computational methods will be applied to analyze and control dynamic behaviors in population systems, including inducing synchronization patterns, decoding spatial and temporal information in complex networks, and revealing driving mechanisms of heterogeneous responses in cancer cell signaling networks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.