Data-guided Control: Fundamental Limits in Presence of Nonlinearities, Streaming Data, and Networks

数据导向控制是系统科学中的一个新兴领域，旨在将时间序列数据作为其控制动态系统的核心结构-取代或补充其模型。该项目解决了当前数据导向控制技术中存在的基本差距。这种方法是多管齐下的；一方面，通过促进其在非线性系统和轨迹漏斗以及大规模网络系统中的应用，扩展了当前的范式。另一方面，开发了在线流数据控制的基本系统理论结构。该项目还有一个重要的教育组成部分。PI将在华盛顿大学开发和重新设计一些控制课程，提供关于动态系统的补充“数据模型”观点。这些课程将鼓励对机器学习感兴趣的学生欣赏基于模型的设计的理论基础。与此同时，该项目的教育目标包括激发对系统和控制理论感兴趣的学生，从植根于系统理论的角度重新审视数据指导的分析，同时包括数据、统计和优化如何显著补充传统的系统和控制培训。该项目有助于使系统理论概念在复杂网络、基础设施系统和卫生保健等领域与数据分析工具和方法一样相关和有用。另一个设想是重振学生对系统和控制的更深层次的欣赏，这些学生在过去十年中被机器学习所吸引。这种新的观点也有助于通过将其范围扩大到第一原理模型既不可用也不合理的领域来吸引新的学生群体。该项目将为动态系统开发新的数据参数化分析和综合技术。基于信息性和威廉基本引理的概念，数据参数化矩阵不等式的使用在非线性轨迹跟踪中的干扰和漏斗合成中进行了检查。接下来，将检查尺度定律，澄清亚最优度量和设计目标的分析属性之间的关系，以及分析和综合所需的数据快照。然后，该项目将检查由流数据驱动的控制综合的新系统理论概念，以及严格确定网络和多代理系统控制的数据简化技术的作用。该项目的首要目标是开发数据导向的系统理论技术，以透明地捕获在线控制中模型和数据之间的“二元性”。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。

Data-guided control is an emerging area in system sciences that aims to embrace time series data as its core construct for control of dynamic systems–replacing or complementing their models. This project addresses foundational gaps in the current state of the art in data-guided control. The approach is multi-pronged; on one hand, the current paradigm is extended by facilitating its applications in the context of nonlinear systems and trajectory funnels, as well as large-scale networked systems. On the other hand, foundational system-theoretic constructs for control with online streaming data are developed. The project also has a significant educational component. The PI will develop and re-design a number of control courses at the University of Washington, providing a complementary “data-model” perspective on dynamic systems. These courses will encourage students with interest in machine learning to appreciate the theoretical underpinnings of model-based design. In parallel, the educational goals of this project involve inspiring students with interest in systems and control theory to re-examine data-guided analysis from a perspective that is rooted in system theory, yet embraces how data, statistics, and optimization significantly complement the more traditional training in systems and control. This project contributes to making system-theoretic concepts in areas such complex networks, infrastructure systems, and health care, as relevant and useful as data analytic tools and methods. Also envisioned is reviving a deeper appreciation for systems and control in students who have gravitated towards machine learning in the past decade. This new perspective also facilitates attracting a new cohort of students to systems by broadening its scope to realms where first-principle models are neither available nor justifiable. The project will develop novel data-parameterized analysis and synthesis techniques for dynamic systems. Building on the notions of informativity and Willem’s Fundamental Lemma, the use of data-parameterized matrix inequalities is examined in the presence of disturbances and for funnel synthesis in nonlinear trajectory-following. Next, scaling laws will be examined that clarify the relation between suboptimality measures and analytic properties of design objectives on one hand, and data-snapshots required for analysis and synthesis on the other. The project will then examine new system-theoretic notions for control synthesis motivated by streaming data, as well as rigorously identify the role of data-reduction techniques for the control of networked and multi-agent systems. The overarching goal of the project is developing data-guided system-theoretic techniques that transparently capture the “duality” between models and data in online control.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.