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.
Many critical national infrastructure and engineering systems are complex dynamical systems composed of numerous components and subject to disturbances. Efficient estimation of these components and detection of disturbances will help practitioners and engineers better predict system dynamics in a timely manner to avoid imminent threats or hazardous effects. However, the interaction between estimation process and complex dynamics leads to a number of challenges in both estimation theory/statistics and systems/control theory. In this project, techniques from systems and control as well as nonparametric statistics are exploited to address challenging estimation and detection issues in dynamical systems. Specifically, the major goals of this project are twofold: (1) efficient estimation and performance analysis of complex components, which are often nonlinear and subject to shape constraints; and (2) understand and characterize complex dynamical behaviors with an eye toward improving estimation efficiency. Intellectual Merit: 1. Estimation of complex components and performance analysis. Many components are nonlinear with varying smoothness and subject to (inequality) shape constraints. By exploring techniques from constrained optimization, asymptotic theory of nonparametric statistics, and ODE theory, we have developed several estimation schemes and analyzed their statistical performance, such as uniform convergence and optimal convergence rates. Our results demonstrate effectiveness of the proposed estimation schemes. 2. Semitstability and L2-gain analysis and computation of distributed multi-agent systems. Distributed multi-agent systems, e.g. large-scale sensor network systems, are widely used in threat detection. To analyze the performance of these systems and related algorithms, we have exploited semistability and L2-gain techniques to develop efficient numerical schemes to characterize and evaluate system performance. 3. Finite-time switching behaviors of nonsmooth dynamical systems. Many dynamical systems in engineering demonstrate switching and hybrid behaviors, and such behaviors on finite time are critical to numerical computation and system analysis and design. In this project, we have established finite switching properties on finite time (i.e., non-Zenoness) when systems are subject to parameter and initial state variations for a class of nonsmooth dynamical systems. 4. Applications. The proposed algorithms and estimation schemes are applied to consensus schemes for distributed multi-agent systems, large-scale sensor networks, PageRank algorithms, range expansion estimation of imported fire ants, and highly nonlinear components with fast varying smoothness in biomedical systems. Broader Impacts: 1. This grant supported Teresa Lebair (Ph.D. student of the PI) to attend several conferences and present her research results. And it also supported summer research of an undergraduate (Suvari Das) at UMBC. Suravi carried out research on estimation of genetic networks under the PI's guidance. 2. The PI has promoted student interests and activities in STEM areas. As a faculty advisor of two student societies/chapters, the PI has greatly contributed to events that have inspired students interests and benefited their career developments in science and engineering at both undergraduate and graduate levels. The PI has been involved in the 3rd SIAM Mid-Atlantic Regional Applied Math Student Conference in 2012 as a co-organizer (representing the SIAM Chapter at UMBC).
