May 8 (Mon) @ 1:30pm: "Numerical Level Set Methods for High-Dimensional Dynamical Systems," Matthew R. Kirchner, ECE PhD Defense

Date and Time
Harold Frank Hall (HFH), Rm 4164 (ECE Conf. Rm.)


This defense presents recent results in developing numerical solutions to certain classes of the Hamilton-Jacobi (HJ) equations as they relate to computing reachable sets of dynamic systems and optimal vehicle trajectories. Many interesting problems can use this solution framework including multiple vehicle coordination, environment exploration and information collection, and collaborative pursuit-evasion. It is especially useful for safety critical applications such as reactive collision avoidance and autonomous emergency landing of aircraft. Specific HJ equations form a theoretical basis that precisely characterize both safe and unsafe operating conditions, necessitating the rapid computation of these solutions for safety critical operations, where a vehicle must react to unforeseen events in the environment.

HJ equations have had limitations in the past for computing usable solutions due to poor scaling with respect to system dimension. This was as a result of the fact that a spatial grid had to be constructed densely in each dimension. Creating equivalent formulations that no longer require spatial grids is the goal of the research and leads to methods that can execute in real-time on embedded hardware.


Matthew R. Kirchner received his B.S. in Mechanical Engineering from Washington State University in 2007 and his M.S. in Electrical Engineering from the University of Colorado at Boulder in 2013. In 2007 he joined the Naval Air Warfare Center Weapons Division in the Navigation and Weapons Concepts Develop Branch. In 2012 he transferred into the Physics and Computational Sciences Division in the Research and Intelligence Department as a research scientist and serving as principal investigator for efforts funded by contracts from the Office of Naval Research, Office of Secretary of Defense (OSD) and elsewhere. He is currently a Ph.D. candidate studying Electrical and Computer Engineering at the University of California, Santa Barbara.

He was the recipient of a Naval Air Warfare Center Weapons Division Graduate Academic Fellowship from 2010 to 2012, in 2011 was named a Paul Harris Fellow by Rotary International, and in 2021 was awarded a Robertson Fellowship from the University of California in recognition of an outstanding academic record. In additional to authoring or co-authoring a dozen research articles, he holds 3 patents from the US Patent and Trademark Office (2 public). His research interests include level set methods for optimal control, differential games, and reachability; multi-vehicle robotics; nonparametric signal and image processing; and navigation and flight control. In August of 2023 he will join the faculty at Auburn University as a tenure-track assistant professor in the Electrical and Computer Engineering Department.

Hosted by: Professor João P. Hespanha

Submitted by: Matthew R. Kirchner <>