ATD: Collaborative Research: Estimation of Nonlinear Components and Disturbances in Dynamical Systems with Applications to Threat Detection

该项目旨在开发有效的统计算法来估计复杂的动力学、非线性分量和扰动，并应用于工程和生物系统中的威胁检测。将解决四个相互关联的研究任务：（1）动力系统的部分状态估计； (2) 具有变化粗糙度的函数的自适应平滑样条估计； (3)形状限制函数的P样条估计； (4)电力系统、遗传网络和工程系统的估计和威胁检测。通过集成渐近统计、优化和控制理论的新技术，将开发出理论上合理且高效的检测算法，并将其应用于潜在的变革系统。许多关键的国家基础设施和重要的工程或生物系统由众多组件组成，并且不断受到干扰。这些组件的故障和/或危险干扰会对国家安全、经济和健康构成威胁。该项目的成功将使从业者能够更好地预测系统动态和迫在眉睫的威胁，从而避免潜在的破坏性后果。特别是，它将有助于检测电力系统中的不利扰动，加深对流行病疾病动力学行为的理解，并提高航空航天和其他工程系统的精度和可靠性。研究人员还将积极开展各种教育和外展活动，让各级学生参与进来，以加强和扩大对科学、技术、工程和数学的认识。

This project aims to develop efficient statistical algorithms for estimation of complex dynamics, nonlinear components and disturbances, with applications to threat detection in engineering and biological systems. Four interconnected research tasks will be addressed: (1) partial state estimation of dynamical systems; (2) adaptive smoothing spline estimation of functions with varying roughness; (3) P-spline estimation of shape restricted functions; and (4) estimation and threat detection of power systems, genetic networks, and engineering systems. By integrating novel techniques from asymptotic statistics, optimization and control theory, theoretically sound and efficient detection algorithms will be developed and be applied to potentially transformative systems.A number of critical national infrastructure and important engineering or biological systems consist of numerous components and are constantly subject to disturbances. The failure of these components and/or hazardous disturbances pose threats to national security, economy and health. The success of this project will allow practitioners to better predict system dynamics and imminent threats, and therefore to avoid potentially damaging consequences. In particular, it will be useful for detecting adverse disturbances in power systems, deepen the understanding of dynamical behaviors of epidemiological diseases, and improve precision and reliability of aerospace and other engineering systems. The investigators will also actively pursue various educational and outreach activities by engaging students at all levels to strengthen and broaden awareness of science, technology, engineering, and mathematics.