Collaborative Research: Structural Frameworks for Output Control of Continuum Ensemble Systems

合作研究：连续系综系统输出控制的结构框架

• 批准号: 2303220
• 负责人: Xudong Chen
• 金额: $ 25.06万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2023-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2303220&HistoricalAwards=false
• 关键词: Collaborative; Research; Structural; Frameworks; Output

Ensemble control is about using a common control input to simultaneously steer a large population (in the limit, a continuum) of dynamical systems. These dynamical systems can themselves be networked multi-agent systems. Because the framework is by nature resilient and scalable, ensemble control finds many applications across various disciplines in science and engineering, ranging from quantum spin systems to neuroscience, emergent behavior, and multi-robot control. Many existing works in this area have focused on the problem of controlling an ensemble system as a whole. However, one is often interested in only controlling a certain output function, such as the mean. At the current stage, little is known for output control of an ensemble system. This project aims to fill the gap. The goal of the project is to establish new tool and results to usher in a framework for output control of continuum ensemble systems. The research program will integrate ideas from multiple areas in mathematics, such as control theory, graph theory, Lie theory, functional analysis, and dynamical systems. The research findings of this project will thus push forward the development of all these research areas. The focus on continuum ensembles of networked systems makes the output control framework adaptable to address problems in various application domains as mentioned above.This project will revolve around several central objects, namely, the output function associated with an ensemble system, the sparsity pattern shared by the individual systems, the geometry of the parameterization space, and the type of system dynamics. Specifically, the PIs will formulate two complementary research thrusts targeting two important classes of output functions and investigate their relations with the other objects: (1) In the first thrust, the PIs will introduce and address a new controllability notion for ensemble systems, termed sub-profile controllability. Roughly speaking, a sub-profile of an ensemble system can be understood as the collection of certain substates of the individual systems. Amongst others, the PIs will aim to establish necessary and sufficient conditions for a sub-profile to be controllable and to develop algorithms for testing. (2) In the second thrust, the PIs will study output functions that integrate individual systems of an ensemble system. Typical examples of such output functions include the average and, more generally, higher moments. The research findings of this thrust will provide insights for the problem of understanding the statistical properties of dynamic profiles over continuum parametrization space.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.

集合控制是关于使用共同的控制输入来同时引导动态系统的大量人群（限制，连续体）。这些动态系统本身可以是网络多代理系统。由于该框架本质上是弹性和可扩展的，因此集成控制在科学和工程中找到了许多在各个学科的应用，从量子旋转系统到神经科学，新兴行为和多机器人控制。该领域的许多现有作品都集中在控制整体系统的问题上。但是，人们通常只对控制特定输出功能（例如均值）感兴趣。在当前阶段，集合系统的输出控制知之甚少。该项目旨在填补空白。该项目的目的是建立新工具和结果，以迎接连续集合系统输出控制的框架。该研究计划将整合数学中多个领域的思想，例如控制理论，图理论，谎言理论，功能分析和动态系统。因此，该项目的研究结果将推动所有这些研究领域的发展。对网络系统的连续集合的关注使输出控制框架可适应如上所述解决各个应用程序域中的问题。该项目将围绕几个中心对象围绕着几个中心对象，即，与集合系统相关的输出功能，由单个系统共享的稀疏模式，参数的几何形状，参数化空间的几何形状以及系统动力学的类型。具体而言，PI将制定两个针对两个重要类别功能类别的互补研究推力，并研究它们与其他对象的关系：（1）在第一个推力中，PIS将引入并解决了对集合系统的新的可控性概念，称为亚副作用可控性。粗略地说，整体系统的次要功能可以理解为单个系统某些取代的集合。除其他外，PI将旨在建立必要和充分的条件，使子Pro构件可控制并开发用于测试的算法。 （2）在第二个推力中，PI将研究整合集合系统各个系统的输出功能。此类输出功能的典型示例包括平均值和更一般的较高力矩。这项推力的研究结果将为理解连续参数化空间的动态概况的统计特性的问题提供见解。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛影响的审查标准通过评估来通过评估来获得支持的。