mlsanityData to 14 Oct 2026

Sample Efficient Certification of Discrete-Time Control Barrier Functions

arXiv 2509.03899 ↗First posted 4 Sep 2025eess.SY cs.LG cs.SYcited by 0

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Abstract (arXiv)

Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs generally involves addressing a complex robust optimization problem, which can be intractable. Scenario-based methods have been proposed to simplify this computation. Then, one needs to verify if the CBF actually satisfies the robust constraints. We present an approach to perform this verification that relies on Lipschitz arguments, and forms the basis of a certification algorithm designed for sample efficiency. Through a numerical example, we validated the efficiency of the proposed procedure.

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References · 18

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2013Intriguing properties of neural networkscited by 5,155
  3. 2019Control Barrier Functions: Theory and Applicationscited by 372
  4. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 328
  5. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  6. 2021Safe Reinforcement Learning Using Robust Control Barrier Functionscited by 59
  7. 2020Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Functioncited by 49
  8. 2020Learning Stability Certificates from Datacited by 45
  9. 2021Predictive control barrier functions: Enhanced safety mechanisms for learning-based controlcited by 14
  10. 2023Exact Verification of ReLU Neural Control Barrier Functionscited by 14
  11. 2021Verification and Synthesis of Control Barrier Functionscited by 13
  12. 2019Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functionscited by 11
6 more
  1. 2024Verification-Aided Learning of Neural Network Barrier Functions with Termination Guaranteescited by 7
  2. 2022Safety Verification and Controller Synthesis for Systems with Input Constraintscited by 4
  3. 2022Compatibility checking of multiple control barrier functions for input constrained systemscited by 2
  4. 2022Fast Verification of Control Barrier Functions via Linear Programmingcited by 1
  5. 2023Computing Controlled Invariant Sets of Nonlinear Control-Affine Systemscited by 1
  6. 2023VBOC: Learning the Viability Boundary of a Robot Manipulator using Optimal Controlcited by 1

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