5 papers · 1 filter
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…