mlsanityData to 7 Oct 2026

Robustness of Control Barrier Functions for Safety Critical Control

arXiv 1612.01554 ↗First posted 5 Dec 2016math.OC cs.SY eess.SYcited by 29

Not on the map. Why?

Abstract (arXiv)

Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lyapunov functions in order to enable controller synthesis for stabilization tasks. A control barrier function enables controller synthesis for safety requirements specified by forward invariance of a set using a Lyapunov-like condition. This paper develops several important extensions to the notion of a control barrier function. The first involves robustness under perturbations to the vector field defining the system. Input-to-State stability conditions are given that provide for forward invariance, when disturbances are present, of a "relaxation" of set rendered invariant without disturbances. A control barrier function can be combined with a control Lyapunov function in a quadratic program to achieve a control objective subject to safety guarantees. The second result of the paper gives conditions for the control law obtained by solving the quadratic program to be Lipschitz continuous and therefore to gives rise to well-defined solutions of the resulting closed-loop system.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Dec 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 5; 2023: 4; 2024: 8; 2025: 3; 2026: 4.

29 papers.

Sort:

By area:

  1. 2021Safe Reinforcement Learning Using Robust Control Barrier Functionscited by 44
  2. 2023Iterative Reachability Estimation for Safe Reinforcement Learningcited by 33
  3. 2024Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformerscited by 29
  4. 2022ISAACS: Iterative Soft Adversarial Actor-Critic for Safetycited by 24
  5. 2021Learning Robust Output Control Barrier Functions from Safe Expert Demonstrationscited by 19
  6. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
  7. 2021Learning Robust Hybrid Control Barrier Functions for Uncertain Systemscited by 14
  8. 2024Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imaginationcited by 12
  9. 2021BarrierNet: A Safety-Guaranteed Layer for Neural Networkscited by 11
  10. 2024Dynamic Model Predictive Shielding for Provably Safe Reinforcement Learningcited by 11
  11. 2023Online Control Barrier Functions for Decentralized Multi-Agent Navigationcited by 10
  12. 2021Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functionscited by 8
17 more
  1. 2025Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Controlcited by 7
  2. 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
  3. 2022Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verificationcited by 3
  4. 2022FI-ODE: Certifiably Robust Forward Invariance in Neural ODEscited by 3
  5. 2022Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functionscited by 2
  6. 2022Risk-Awareness in Learning Neural Controllers for Temporal Logic Objectivescited by 1
  7. 2023EnergyShield: Provably-Safe Offloading of Neural Network Controllers for Energy Efficiencycited by 1
  8. 2024Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Modelscited by 1
  9. 2023CaRT: Certified Safety and Robust Tracking in Learning-based Motion Planning for Multi-Agent Systemscited by 0
  10. 2024Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attackscited by 0
  11. 2024Scaling Learning based Policy Optimization for Temporal Logic Tasks by Controller Network Dropoutcited by 0
  12. 2025Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functionscited by 0
  13. 2025Tail-Safe Hedging: Explainable Risk-Sensitive Reinforcement Learning with a White-Box CBF--QP Safety Layer in Arbitrage-Free Marketscited by 0
  14. 2026Safe Probabilistic Planning for Human-Robot Interaction using Conformal Risk Controlcited by 0
  15. 2026Sustaining AI safety: Control-theoretic external impossibility, intrinsic necessity, and structural requirementscited by 0
  16. 2026Robust Koopman Control Barrier Filters for Safe Actor-Critic Reinforcement Learningcited by 0
  17. 2026LEAP-CBF: A Safety Filter for Uncertain Systems with Least-Effort Adversarial Potentialscited by 0