William Sharpless

Hello,

I am a Mechanical and Aerospace PhD candidate in Sylvia Herbert's Safety and Autonomous Systems group at UC San Diego.

My work involves differential games (HJB-PDE's), control and learning, and my thesis concentrates on feasible methods for safe, high-dimensional autonomy. I am an HHMI/NIH Interfaces fellow, and I am also supported by the ONR and the Society of Hellman.

Before, I did my undergraduate degree in applied mathematics at UC Berkeley where I worked with Claire Tomlin, Adam Arkin and Jay Keasling.

willsharpless [at] ucsd [dot] edu  /  CV  /  Google Scholar  /  Github  /  Linkedin

profile photo
Publications
Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games
William Sharpless, Zeyuan Feng, Somil Bansal, Sylvia Herbert.
Submitted to L4DC - December, 2024

Here, we show that to learn a nonlinear HJ-PDE for autonomy, one may introduce the linear solution for ~25x increase in accuracy and ~20x acceleration in training for problems up to 50-dimensions.

[paper]

State-Augmented Linear Games with Antagonistic Error for High-Dimensional, Nonlinear Hamilton-Jacobi Reachability
William Sharpless, Yat Tin Chow, Sylvia Herbert.
Conference on Decision and Control - March, 2024

Here, we propose a novel, lifted differential game that is guaranteed to be conservative, is solved rapidly, and allows the use of lifting functions such as neural nets, polynomials and radial basis functions to reduce linear error.

[paper]

Conservative Linear Envelopes for High-Dimensional, Hamilton-Jacobi Reachability for Nonlinear Systems via the Hopf Formula
William Sharpless, Yat Tin Chow, Sylvia Herbert.
Transactions on Automatic Control (In Review) - April, 2024

Here, we demonstrate how the error between a nonlinear system of interest and a linearization of it may transformed into an antagonistic player, yielding a conservative linear game that may be solved rapidly in high-dimensions.

[paper]

Koopman-Hopf Hamilton-Jacobi Reachability and Control
William Sharpless, Nikhil Shinde, Matthew Kim, Yat Tin Chow, Sylvia Herbert.
Arxiv (In Review) - November, 2023

In this work, we propose and demonstrate the use of Koopman linearizations to allow the use of the Hopf formula for linear differential games to yield a performant algorithm for high-dimensional, nonlinear autonomy.

[paper]

Invited Talks
American Math Society (AMS) - Session on Applied Partial Differential Equations, October 2024 [slides]
Lifted Differential Games with Antagonistic Error for Fast, Accurate and Conservative HJB Approximations.
Scientific AI Research Seminar @ Oden Institute - UT Austin, October 2024 [slides]
Lifted Differential Games with Antagonistic Error for Fast, Accurate and Conservative HJB Approximations.
Society of Industrial and Applied Mathematics (SIAM) - High Dimensional Control and HJE Session, September 2024 [slides]
Lifted Differential Games with Antagonistic Error for Fast, Accurate and Conservative HJB Approximations.
Safe and Intelligent Autonomy Seminar @ USC, August 2023 [slides]
Conservative Envelopes with Linear Hopf Solutions for Fast & Safe High-Dimensional Control and Reachability
Level Set Seminar @ UCLA, April 2023 [slides]
Koopman-Hopf Hamilton-Jacobi-Reachability for Fast and Accurate Autonomy
Software
HopfReachability.jl

Julia software for accelerated non-smooth, convex optimization of the Hopf objective for solving high-dimensional differential games.


Website template by Jon Barron (source code).
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