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

复杂系统是由孤立的或相互作用的动力学成分组成的，在自然界和人类社会中普遍存在。这类系统的显著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、电力分配和工程中的交通控制系统。因此，不仅针对一个动力系统，而且针对大量几乎相同的动力单元的整个种群来处理控制和估计任务已经成为许多科学和工程领域中反复出现的主题，并且动态种群的精确有针对性的协调和估计的能力将打开闸门，以在各种各样的尖端应用中取得快速和显著的进步。处理动态种群的基本困难在于控制和观察只能在种群水平上实现，即，分别通过向群体中的所有系统广播单个输入信号以及通过接收群体中的系统的聚集测量，并且对于这种新的群体系统类别，基本上缺乏原则性的控制和观测策略。因此，以人口为基础的技术仍然远远没有充分发挥其潜力。本研究的目的是建立一个通用的和连贯的理论和计算框架的各种新兴的应用程序，严重依赖于一个有针对性的协调大量人口的动力系统，从而关闭当前理论和实践之间的差距，在新兴的应用问题与人口系统有关。拟议的研究将为系统理论、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。通过华盛顿大学的学校伙伴关系研究所，将共同努力吸引代表性不足的群体和妇女参加研究计划，并使公众和大学前K-12学生参与科学研究。该项目将系统地研究广播信号可控性的基本问题，以及相对于群体中系统的聚集测量的可观测性，并开发最优控制策略，该策略将使得能够实现群体中动态结构的有针对性的协调。通过桥接形式系统理论，系综控制技术，应用代数和几何与计算工程，一般和通用的人口控制框架将制定。具体来说，控制分析和设计将通过利用高度不明显但从根本上密切联系到不同的领域，包括可控性的多项式近似和可观测性的数学层析成像来进行。对这些新联系的探索将拓宽理论和计算工作的范围，以理解复杂种群系统和网络的机制和集体行为。此外，所发展的理论和计算方法将被应用于分析和控制种群系统中的动态行为，包括诱导同步模式，解码复杂网络中的空间和时间信息，该奖项反映了NSF的法定使命，并通过使用基金会的知识产权进行评估，被认为值得支持。优点和更广泛的影响审查标准。

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.