mlsanityData to 7 Oct 2026

Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraints

arXiv 1410.6445 ↗First posted 23 Oct 2014math.OCcited by 41

Not on the map. Why?

Abstract (arXiv)

We consider a reach-avoid differential game, in which one of the players aims to steer the system into a target set without violating a set of state constraints, while the other player tries to prevent the first from succeeding; the system dynamics, target set, and state constraints may all be time-varying. The analysis of this problem plays an important role in collision avoidance, motion planning and aircraft control, among other applications. Previous methods for computing the guaranteed winning initial conditions and strategies for each player have either required augmenting the state vector to include time, or have been limited to problems with either no state constraints or entirely static targets, constraints and dynamics. To incorporate time-varying dynamics, targets and constraints without the need for state augmentation, we propose a modified Hamilton-Jacobi-Isaacs equation in the form of a double-obstacle variational inequality, and prove that the zero sublevel set of its viscosity solution characterizes the capture basin for the target under the state constraints. Through this formulation, our method can compute the capture basin and winning strategies for time-varying games at no additional computational cost with respect to the time-invariant case. We provide an implementation of this method based on well-known numerical schemes and show its convergence through a simple example; we include a second example in which our method substantially outperforms the state augmentation approach.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Oct 2014.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 6; 2023: 5; 2024: 10; 2025: 10; 2026: 2.

41 papers.

Sort:

By area:

  1. 2023The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systemscited by 77
  2. 2024Agile But Safe: Learning Collision-Free High-Speed Legged Locomotioncited by 53
  3. 2025Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysiscited by 44
  4. 2021Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learningcited by 43
  5. 2023Iterative Reachability Estimation for Safe Reinforcement Learningcited by 33
  6. 2022Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guaranteescited by 24
  7. 2022ISAACS: Iterative Soft Adversarial Actor-Critic for Safetycited by 24
  8. 2021Safe Occlusion-aware Autonomous Driving via Game-Theoretic Active Perceptioncited by 22
  9. 2022Safe Model-Based Reinforcement Learning with an Uncertainty-Aware Reachability Certificatecited by 16
  10. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
  11. 2021Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal controlcited by 12
  12. 2024Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imaginationcited by 12
29 more
  1. 2022Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertaintycited by 11
  2. 2024Hamilton-Jacobi Reachability in Reinforcement Learning: A Surveycited by 11
  3. 2021Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachabilitycited by 10
  4. 2025Real-Time Out-of-Distribution Failure Prevention via Multi-Modal Reasoningcited by 10
  5. 2023Deception Game: Closing the Safety-Learning Loop in Interactive Robot Autonomycited by 9
  6. 2021Analyzing Human Models that Adapt Onlinecited by 8
  7. 2024To the Max: Reinventing Reward in Reinforcement Learningcited by 7
  8. 2024Human-AI Safety: A Descendant of Generative AI and Control Systems Safetycited by 7
  9. 2022Infinite-Horizon Reach-Avoid Zero-Sum Games via Deep Reinforcement Learningcited by 6
  10. 2021Correct-by-construction reach-avoid control of partially observable linear stochastic systemscited by 5
  11. 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
  12. 2021Deep Reinforcement Learning-based UAV Navigation and Control: A Soft Actor-Critic with Hindsight Experience Replay Approachcited by 3
  13. 2022A Survey of Decision Making in Adversarial Gamescited by 3
  14. 2024Pontryagin Neural Operator for Solving Parametric General-Sum Differential Gamescited by 3
  15. 2025Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networkscited by 3
  16. 2025Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environmentscited by 3
  17. 2021Towards Data-Driven Synthesis of Autonomous Vehicle Safety Conceptscited by 2
  18. 2025Your Learned Constraint is Secretly a Backward Reachable Tubecited by 2
  19. 2025Dual-Objective Reinforcement Learning with Novel Hamilton-Jacobi-Bellman Formulationscited by 2
  20. 2025Hierarchical Vision Language Action Model Using Success and Failure Demonstrationscited by 2
  21. 2025From Refusal to Recovery: A Control-Theoretic Approach to Generative AI Guardrailscited by 1
  22. 2026Value Functions for Temporal Logic: Optimal Policies and Safety Filterscited by 1
  23. 2023Learned Risk Metric Maps for Kinodynamic Systemscited by 0
  24. 2023Correct-by-Construction Control for Stochastic and Uncertain Dynamical Models via Formal Abstractionscited by 0
  25. 2024Tackling Decision Processes with Non-Cumulative Objectives using Reinforcement Learningcited by 0
  26. 2024Gait Switching and Enhanced Stabilization of Walking Robots with Deep Learning-based Reachability: A Case Study on Two-link Walkercited by 0
  27. 2025Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllerscited by 0
  28. 2025Reach-Avoid Differential game with Reachability Analysis for UAVs: A decomposition approachcited by 0
  29. 2026TAIL-Safe: Task-Agnostic Safety Monitoring for Imitation Learning Policiescited by 0