11 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…
Value Functions for Temporal Logic: Optimal Policies and Safety Filters
Oswin So, William Sharpless, Sylvia Herbert +1
While Bellman equations for basic reach, avoid, and reach-avoid problems are well studied, the relationship between value optimality and policy optimality becomes subtle in the und…
Bellman Value Decomposition for Task Logic in Safe Optimal Control
William Sharpless, Oswin So, Dylan Hirsch +2
Real-world tasks involve nuanced combinations of goal and safety specifications. In high dimensions, the challenge is exacerbated: formal automata become cumbersome, and the combin…
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…
State-Augmented Linear Games with Antagonistic Error for High-Dimensional, Nonlinear Hamilton-Jacobi Reachability
Will Sharpless, Yat Tin Chow, Sylvia Herbert
Hamilton-Jacobi Reachability (HJR) is a popular method for analyzing the liveness and safety of a dynamical system with bounded control and disturbance. The corresponding HJ value…
Conservative Linear Envelopes for Nonlinear, High-Dimensional, Hamilton-Jacobi Reachability
Will Sharpless, Yat Tin Chow, Sylvia Herbert
Hamilton-Jacobi reachability (HJR) provides a value function that encodes the set of states from which a system with bounded control inputs can reach or avoid a target despite any…