FOUNDATIONS OF GEOMETRIC AND DATA-DRIVEN ENSEMBLE CONTROL
Abstract
The objective of this project is to pioneer new geometric and data-driven methodologies for a holistic understanding and treatment of increasingly complicated and high-dimensional dynamic population systems. The rapid increase in the growing complexity and scale of systems and access to affordable ubiquitous computing power and measurement data in the age of Big Data are presenting both unprecedented opportunities and challenges in the field of dynamics and control. In the wake of this ongoing trend, the research landscape in this long-standing area is experiencing a considerable shift from the purely analytic study of moderately complicated first-principles models to pursuit of integrated approaches involving data-driven perspectives and techniques for complex and large-scale system models. This transition is in response to tackling increasingly convoluted systems and system descriptions, as well as widely emerging high-level tasks such as modeling and controlling the brain or analyzing human behavior and dynamics in a social network. In this research, strenuous efforts will be made to push the boundaries of theory and applications in control of high-dimensional and ensemble systems by leveraging the power of geometry and recent advances in data science and learning. A major distinctive feature of our innovations is not only to enrich existing model-based approaches by deeply exploiting the algebraic and geometric structures of the system dynamics, but also directly incorporate data in the analysis and synthesis of control systems with desired guarantees. The proposed research will establish a rigorous integrated control-theoretic and data-driven framework that provides a systematic and mathematically grounded approach to conduct ensemble control analysis and design by using tools from differential geometry, algebraic topology, representation theory, operator theory, geometric control theory, and machine learning. Moreover, the resulting work will also support the infrastructure of interdisciplinary research by building blocks for analyzing and controlling ensemble systems arising in cutting-edge areas.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 21, 2022
- Source ID
- FA95502110335XX0
Entities
People
- Jr-Shin Li
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- Washington University in St. Louis