CAREER: Resilient and Scalable Framework for Control of Mutli-agent Systems: Ensemble Control of Network Motifs

这个NSF CAREER项目旨在开发一个新的框架，用于控制多智能体系统，该系统本质上具有弹性和可扩展性。该框架背后的想法很简单：控制一个大网络，而不是控制一个大网络，控制一个小网络的大量人口。该项目将为控制大型复杂系统带来革命性的变化，通过使用单个控制输入来同时控制任意数量的网络控制系统。这将通过集成控制理论和网络控制理论来实现。该项目的智力价值包括开发一套原始的方法，并建立新的控制理论的结果，控制网络系统的无限合奏。该项目更广泛的影响包括在数学和多智能体系统研究之间建立新的联系，使拟议的框架能够在量子系统、无人机系统和机器人技术等各个领域使用，并开发新课程，为下一代学生提供先进的数学工具和工程方法。为了建立所提出的控制框架，PI将研究由无限多个网络控制系统组成的集成系统。在合奏中的各个网络系统可以共享共同的信息流拓扑结构，但显示的系统参数的变化是由连续参数化空间中的点索引。一个主要的技术挑战是，人们只能使用有限维的，共同的控制输入，以引导一个连续体合奏的个人控制系统。此外，这些单独的系统受到信息流拓扑结构的约束。这种挑战在文献中尚未得到解决。因此，为了发展所提出的控制框架，PI将：（1）建立新的概念，如模体的集成，并制定新的问题，如结构集成可控性;（2）建立必要和/或充分条件的信息流拓扑的个别网络系统，可以包括一个可控的集成;（3）建立对单个系统的物理动力学，信息流拓扑学，和几何参数化空间的集合可控性和各种类型的输出可控性。这个奖项反映了NSF的法定使命，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。

This NSF CAREER project aims to develop a novel framework for control of multi-agent systems that is by nature resilient and scalable. The idea behind the framework is simple to state: instead of controlling a large network, one controls a large population of small ones. The project will bring transformative change for controlling large-scale complex systems by enabling the use of a single control input to simultaneously steer an arbitrarily large number of networked control systems. This will be achieved by integrating both ensemble control theory and networked control theory. The intellectual merits of the project include developing an original set of methodologies and establishing novel control-theoretical results for controlling infinite ensembles of networked systems. The broader impacts of the project include establishing new connections between mathematics and the study of multi-agent systems, enabling the use of the proposed framework across various domains such as quantum systems, unmanned aerial systems, and robotics, and developing new courses that prepare the next generation of students with advanced mathematical tools and engineering methods. To establish the proposed control framework, the PI will investigate ensemble systems that are composed of infinitely many networked control systems. The individual networked systems in the ensemble may share common information flow topologies, but show variations in system parameters which are indexed by points in a continuum parameterization space. A major technical challenge is that one can only use a finite-dimensional, common control input to steer a continuum ensemble of individual control systems. Moreover, these individual systems are constrained by information flow topologies. Such a challenge has not yet been tackled in the literature. Thus, to develop the proposed control framework, the PI will: (1) establish new concepts, such as ensembles of motifs, and formulate new problems, such as structural ensemble controllability; (2) establish necessary and/or sufficient conditions for information flow topologies of individual networked systems that can comprise a controllable ensemble; (3) establish a deep understanding of the fundamental relation between physical dynamics of individual systems, information flow topology, and geometry of parameterization space for ensemble controllability and for various types of output controllability.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.