Developing Novel Frameworks for Open Hybrid Dynamical Systems

May 1, 2023

Taeyoung Lee

Congratulations to Professor Taeyoung Lee of the Mechanical and Aerospace Engineering Department for receiving an award from the Department of Defense (DoD) as part of the Multidisciplinary University Research Initiative (MURI) Program! Professor Lee was among the 31 awards given for his project, “Unified Large-Scale Theoretical and Computational Frameworks for Invariance and Composition of Open Hybrid Dynamical Systems.”

Hybrid systems are dynamical systems that exhibit both continuous and discrete behaviors. In other words, they are systems that may instantaneously switch between various modes of operation depending on certain events or even randomly. Due to their unifying framework to describe complex behaviors, hybrid systems have been utilized to model a wide range of dynamic systems, such as robotics, biology, chemistry, and social networks.

However, due to the intricate interplay between continuous evolution and instantaneous switching, they manifest complex and rich dynamic characteristics that are challenging, or even formidable, to analyze with conventional apparatuses of dynamic system theory. Through multidisciplinary research that integrates recent developments in applied mathematics, computer science, engineering, and data-driven computational techniques, this project aims to establish both theoretical and computational frameworks to uncover these intriguing behaviors of complicated open hybrid dynamical systems.

Thus, identifying and constructing the inherent structures of hybrid dynamics, such as topological properties and invariances, that can be preserved under interaction with uncertain environments and composition over a complex network is the research objective of this study. The novelty lies in establishing a trustworthy computational foundation that is carefully constructed in conjunction with the underlying geometry, leading to significant generalization capacity and computation efficiency to handle non-trivial and non-conventional hybrid systems.

Creating such a framework is important to the DoD as Lee said, “The MURI award is one of the most prestigious research grants of the DoD which provides valuable long-term funding to support research of strategic importance to the DoD with the potential to lead significant advancements in science and technology.”

A framework for open hybrid dynamical systems is also of interest to the Air Force Office of Scientific Research (AFOSR). AFOSR, alongside the Army Research Office and the Office of Naval Research, solicited proposals in 24 topic areas of strategic importance to the Department. In creating a proposed scalable and composable framework, Lee and his team will provide more accurate, reliable, and efficient algorithms for the modeling, simulation, and design of complex systems; enabling them to complete their mission successfully in support of the Air Force under uncertain, complex, and adversarial environments.

The project period is from May 1, 2023, to the end of April 2028. GW will be leading the team of investigators from the University of Michigan, Rutgers University, and the University of Florida. Out of the total budget of $7.5M, GW’s share is about $1.6M. 

Lee said, “Receiving a DoD MURI award is a significant achievement in my career. More importantly, it is truly exhilarating to be able to focus on fundamental and challenging research questions over the next five years without interruption while exploring and venturing into new areas beyond my current expertise.”