25 citations · 40 across the 15 of their papers we have counts for
15 papers
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…
A Hamilton-Jacobi Reachability Framework with Soft Constraints for Safety-Critical Systems
Chams Eddine Mballo, Donggun Lee, Claire J. Tomlin
Traditional reachability methods provide formal guarantees of safety under bounded disturbances. However, they strictly enforce state constraints as inviolable, which can result in…
A Forward Reachability Perspective on Control Barrier Functions and Discount Factors in Reachability Analysis
Jason J. Choi, Donggun Lee, Boyang Li +4
Control invariant sets are crucial for various methods that aim to design safe control policies for systems whose state constraints must be satisfied over an indefinite time horizo…
Geometry of the twin manifolds of regular semisimple Hessenberg varieties and unicellular LLT polynomials
Young-Hoon Kiem, Donggun Lee
Recently, Masuda-Sato and Precup-Sommers independently proved an LLT version of the Shareshian-Wachs conjecture which says that the Frobenius characteristics of the cohomology of t…
Interaction-Aware Trajectory Planning for Autonomous Vehicles with Analytic Integration of Neural Networks into Model Predictive Control
Piyush Gupta, David Isele, Donggun Lee +1
Autonomous vehicles (AVs) must share the driving space with other drivers and often employ conservative motion planning strategies to ensure safety. These conservative strategies c…
RAMP: A Risk-Aware Mapping and Planning Pipeline for Fast Off-Road Ground Robot Navigation
Lakshay Sharma, Michael Everett, Donggun Lee +3
A key challenge in fast ground robot navigation in 3D terrain is balancing robot speed and safety. Recent work has shown that 2.5D maps (2D representations with additional 3D infor…
Birational geometry of generalized Hessenberg varieties and the generalized Shareshian-Wachs conjecture
Young-Hoon Kiem, Donggun Lee
We introduce generalized Hessenberg varieties and establish basic facts. We show that the Tymoczko action of the symmetric group on the cohomology of Hessenberg varieties ext…
Infinite-Horizon Reach-Avoid Zero-Sum Games via Deep Reinforcement Learning
Jingqi Li, Donggun Lee, Somayeh Sojoudi +1
In this paper, we consider the infinite-horizon reach-avoid zero-sum game problem, where the goal is to find a set in the state space, referred to as the reach-avoid set, such that…
Representations on the cohomology of
Jinwon Choi, Young-Hoon Kiem, Donggun Lee
The moduli space of pointed stable curves of genus admits an action of the symmetric group by permuting the marked points. We provide a…
Towards cyber-physical systems robust to communication delays: A differential game approach
Shankar A. Deka, Donggun Lee, Claire J. Tomlin
Collaboration between interconnected cyber-physical systems is becoming increasingly pervasive. Time-delays in communication channels between such systems are known to induce catas…
Lax Formulae for Efficiently Solving Two Classes of State-Constrained Optimal Control Problems
Donggun Lee, Claire J. Tomlin
This paper presents Lax formulae for solving the following optimal control problems: minimize the maximum (or the minimum) cost over a time horizon, while satisfying a state constr…
Hamilton-Jacobi Equations for Two Classes of State-Constrained Zero-Sum Games
Donggun Lee, Claire J. Tomlin
This paper presents Hamilton-Jacobi (HJ) formulations for two classes of two-player zero-sum games: one with a maximum cost value over time, and one with a minimum cost value over…
A Computationally Efficient Hamilton-Jacobi-based Formula for State-Constrained Optimal Control Problems
Donggun Lee, Claire J. Tomlin
This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the leve…
Robust Control Barrier-Value Functions for Safety-Critical Control
Jason J. Choi, Donggun Lee, Koushil Sreenath +2
This paper works towards unifying two popular approaches in the safety control community: Hamilton-Jacobi (HJ) reachability and Control Barrier Functions (CBFs). HJ Reachability ha…
A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
Margaret P. Chapman, Jonathan Lacotte, Aviv Tamar +7
A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint…