Quantifying Complex Behavior in Large-Scale Systems through Structured Uncertainty Analysis

通过结构不确定性分析量化大系统中的复杂行为由相互作用的动力元素组成的大系统在自然界中无处不在，在工程系统中越来越常见。这类系统的例子包括电网、车辆交通、社交网络等大型网络。这种网络表现出许多复杂的现象，这些现象是由各个组件之间的动态相互作用引起的。对这些现象的定性理解和定量预测是当前科学和工程领域的重大挑战。该奖项支持基于结构化随机不确定性技术开发定量分析方法的研究。这些技术模拟了在不确定环境中运行的大系统，包括外部强迫和攻击以及交互动力学中的内部无序。主要的观察结果是，即使单个不确定性源可能很小，但它们的聚合网络效应可能会很大，甚至是灾难性的，导致网络稳定性或性能的损失。结构化不确定性分析的目的是准确地量化哪种类型的小规模不确定性会导致大规模的网络现象。大动态系统中的不确定性既可以发生在系统参数或结构中，也可以发生在不确定的强迫和扰动中。该研究项目的理论目标是双重的。首先是发展一种统一的方法，一方面解决大规模网络系统的看似不同的问题，另一方面解决用偏微分方程描述的连续统空间上的系统。这两组问题都将被视为空间分布系统，但前者用网络结构来描述离散空间，后者用连续空间来描述。这种理论综合能够以类似于离散时间系统和连续时间系统之间的类比的方式，以类似于但明显丰富的方式来比较两种设置下的结果和方法。第二个目标是开发具有加性和乘性噪声的线性系统的高度可扩展的、无仿真的性能和稳定性测试。将开发专门技术的应用领域是网络/合作控制，其中网络结构和条件都是随机变化的，以及具有随机场系数的流体流动。这种方法论的综合为加性和乘性噪声领域的控制理论奠定了基础。它能够解决不确定系统中的几个问题，这些问题通常是通过昂贵的随机模拟来研究的，因此不能扩展到大规模系统。以统一的方式处理离散和连续空间的能力将允许用偏微分方程描述的不确定网络和系统之间的概念和结果的新综合。

Quantifying Complex Behavior in Large-Scale Systems through Structured Uncertainty AnalysisLarge-scale systems of interacting dynamical elements are ubiquitous in nature and are increasingly common in engineered systems. Examples of such systems include large networks such as the power grid, vehicular traffic, social networks and many more. Such networks exhibit many complex phenomena arising from dynamic interaction between individual components. Qualitative understanding and quantitative prediction of these phenomena is a major current scientific and engineering challenge. This award supports research to develop quantitative analysis methods based on the techniques of structured stochastic uncertainty. These techniques model large-scale systems operating in uncertain environments, which include external forcing and attacks as well as internal disorder in interaction dynamics. The main observation is that even though individual uncertainty sources may be very small, their aggregate network effect may be large and even catastrophic, leading to loss of network stability or performance. Structured uncertainty analysis aims at quantifying exactly which type of small-scale uncertainty could lead to large-scale network-wide phenomena. Uncertainties in large-scale dynamic systems can occur in system parameters or structure as well as in uncertain forcing and disturbances. The theoretical aims of the research program are twofold. The first is to develop a unified approach to the seemingly distinct problems of large-scale networked systems on the one hand, and systems over continuum space described by partial differential equations on the other. These two sets of problems will both be treated as spatially distributed systems, but with discrete space being described by the network structure in the former, and continuum space in the latter. This theoretical synthesis enables a comparative development of results and methods in both settings in a manner similar to, but significantly richer, than analogies between discrete- and continuous-time systems. The second aim is to develop highly-scalable, simulation-free performance and stability tests for linear systems with both additive and multiplicative noise. Application areas for which specialized techniques will be developed are network/cooperative control where both the network structure and conditions are stochastically varying, and fluid flow with stochastic field coefficients. This methodological synthesis contributes to the foundations of Control Theory in the area of additive and multiplicative noise. It enables the solution of several problems in uncertain systems that are typically investigated through expensive stochastic simulations, and are therefore not scalable to large-scale systems. The ability to address discrete and continuum space in a unified manner will allow for a new synthesis of concepts and results between uncertain networks and systems described by partial differential equations.