Problems in Distributed Sensing and Control

当前对分布式控制的兴趣导致了图论思想在分析和综合各种期望行为问题上的应用的迅速增加，如蜂群、集合、达成共识，以及与分布式平均、搜索和救援、环境监测、安全等相关的各种传感和通信任务。虽然结合图论和系统论对这些问题的深入研究已经进行了一段时间，但它很可能在未来几年得到显著扩展。其中一个例子是对结构可控性及其在群体、复杂社会网络和网络安全方面的应用的兴趣的复苏。另一个是对分布式计算程序发展的兴趣激增，用于解决基本的数值问题，如估计线性系统的参数，解决分布式优化问题或解决可能的非线性代数方程系统。还有一个是极其活跃的网络安全领域。从广义上讲，这是本项目将重点关注的三个问题领域。将进行的研究将在三个明确界定的方面解决分布式传感和控制问题。(1)将研究线性动力系统的各种基本性质（如可控性和谱可赋值性）的特定扰动类的通用性。许多经典结果已经存在于线性模型中，其中代数独立的参数在唯一的位置“线性”地进入模型的系统矩阵。本课题研究的新颖之处在于，它旨在处理在多个位置的模型系统矩阵中出现相同参数的常见情况。我们将尝试用图论的术语来描述结构可控性和结构固定模态的更一般的概念。(2)将努力开发分布式和异步算法，用于解决某些非线性代数方程系统，这些方程组与跨给定自主代理网络的分布式优化和估计问题有关，假设代理与时变网络之间的通信有限。将讨论这些算法的收敛速度、鲁棒性和稳定性问题，以及间歇性数据传输和传输延迟的影响。(3)将探索基于博弈论的各种算法，用于在物理网络中搜索，目标是捕获或以其他方式击败意图造成破坏的入侵者。游戏将在两名玩家之间展开，即入侵者和负责阻止入侵者的监视特工。将考虑各种类型的静态和动态游戏。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。

Current interest in distributed control has led to a very rapid increase in the application of graph theoretic ideas to problems of analyzing and synthesizing a variety of desired behaviors such as swarming, rendezvousing, reaching a consensus, as well as well as a variety of sensing and communication tasks associated with distributed averaging, search and rescue, environmental monitoring, security, etc. While this in-depth assault on these problems using a combination of graph theory and system theory has been underway for some time, it is likely to significantly expand in the years to come. One example of this is the resurgence of interest in structural controllability and its applications to swarming, complex social networks and network security. Another is the explosion of interest in the development of distributed computational procedures for addressing basic numerical problems such as estimating parameters of a linear system, solving a distributed optimization problem or solving a system of possibly nonlinear algebraic equations. Still another is the extremely active area of network security. In broad terms these are the three problem areas upon which this project will focus.The research to be undertaken will address distributed sensing and control on three clearly defined fronts. (1) A study will be made of the genericity with respect to specific perturbation classes of various fundamental properties of linear dynamic systems such as controllability and spectrum assignability. Many classical results already exist for linear models in which algebraically independent parameters enter a model's system matrices "linearly" at unique locations. The novelty of the research to be undertaken in this project is that it is aims to deal with the commonly encountered situation in which the same parameter appears in a model's systems matrices in multiple location. An attempt will be made to characterize in graph theoretic terms significantly more general notions of structural controllability and structurally fixed modes than are currently available. (2) An effort will be made to develop distributed and asynchronous algorithms for solving certain systems of nonlinear algebraic equations which arise in connection with distributed optimization and estimation problems across a given network of autonomous agents assuming limited communication between agents and time-varying networks. Questions of convergence rate, robustness and stability of these algorithms will be addressed, as will the effects of intermittent data transmissions and transmission delays. (3) An exploration will be made of various algorithms based on game theory for searching across a physical network with the goal of capturing or otherwise defeating an intruder intent on causing a disruption. The games will be formulated between two players, namely the intruder and a surveillance agent whose job is to thwart the intruder. Various types of static and dynamic games will be considered.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.