8 papers
Exact Decomposition of Value Functions for Two-Player Games in Hamilton-Jacobi Reachability
Dylan Hirsch, William Sharpless, Sylvia Herbert
Hamilton-Jacobi reachability (HJR) is an important framework in safe control theory. HJR provides theoretical tools and numerical methods to obtain value-functions for tasks involv…
Extending and Unifying the Fundamental Tasks of Hamilton-Jacobi Reachability Analysis
Dylan Hirsch, William Sharpless, Donggun Lee +1
In this work, we introduce the generalized reach-avoid (GRA) task, which both extends and unifies the canonical tasks of Hamilton-Jacobi Reachability (HJR). We show that the GRA no…
Exact Decomposition of Adversarial Dual-Objective Value Functions, with Applications to Optimal Drug Dosing
Dylan Hirsch, William Sharpless, Sylvia Herbert
Hamilton-Jacobi Reachability (HJR) is a central framework in safe control theory. While HJR has traditionally focused on a few fundamental tasks, there is increasing interest in sc…
Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Dylan Hirsch, Jaime Fernández Fisac, Sylvia Herbert
Control barrier functions (CBFs) and Hamilton-Jacobi reachability (HJR) are central frameworks in safe control. Traditionally, these frameworks have been viewed as distinct, with t…
MADR: MPC-guided Adversarial DeepReach
Ryan Teoh, Sander Tonkens, William Sharpless +4
Hamilton-Jacobi (HJ) Reachability offers a framework for generating safe value functions and policies in the face of adversarial disturbance, but is limited by the curse of dimensi…
Dual-Objective Reinforcement Learning with Novel Hamilton-Jacobi-Bellman Formulations
William Sharpless, Dylan Hirsch, Sander Tonkens +2
Hard constraints in reinforcement learning (RL) often degrade policy performance. Lagrangian methods offer a way to blend objectives with constraints, but require intricate reward…
Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions
Matthew Kim, William Sharpless, Hyun Joe Jeong +3
Recent developments in autonomous driving and robotics underscore the necessity of safety-critical controllers. Control barrier functions (CBFs) are a popular method for appending…
Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games
William Sharpless, Zeyuan Feng, Somil Bansal +1
As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging i…