Sample Efficient Certification of Discrete-Time Control Barrier Functions

• URL: http://arxiv.org/abs/2509.03899v1
• Date: Thu, 04 Sep 2025 05:47:24 GMT
• Title: Sample Efficient Certification of Discrete-Time Control Barrier Functions
• Abstract summary: Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems.<n>Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets.<n>We present an approach to verify if the CBF actually satisfies the robust constraints.
• Score: 2.4118840512344852
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• A Feasibility-Enhanced Control Barrier Function Method for Multi-UAV Collision Avoidance [8.527260258364894]
  This paper presents a feasibility-enhanced control barrier function (FECBF) framework for multi-UAV collision avoidance.<n>In dense multi-UAV scenarios, the feasibility of the CBF quadratic program (CBF-QP) can be compromised due to internal incompatibility.
  arXiv  Detail & Related papers  (2026-03-13T15:58:40Z)
• CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functions [2.092779643426281]
  Control Barrier Functions (CBFs) are a practical approach for designing safety-critical controllers.<n>Recent efforts have explored learning-based methods, such as neural CBFs, to address this issue.<n>We propose a novel framework that leverages split-conformal prediction to generate formally verified neural CBFs.
  arXiv  Detail & Related papers  (2025-03-18T10:01:06Z)
• Domain Adaptive Safety Filters via Deep Operator Learning [5.62479170374811]
  We propose a self-supervised deep operator learning framework that learns the mapping from environmental parameters to the corresponding CBF. We demonstrate the effectiveness of the method through numerical experiments on navigation tasks involving dynamic obstacles.
  arXiv  Detail & Related papers  (2024-10-18T15:10:55Z)
• Reinforcement Learning-based Receding Horizon Control using Adaptive Control Barrier Functions for Safety-Critical Systems [14.166970599802324]
  Optimal control methods provide solutions to safety-critical problems but easily become intractable.<n>We propose a Reinforcement Learning-based Receding Horizon Control approach leveraging Model Predictive Control.<n>We validate our method by applying it to the challenging automated merging control problem for Connected and Automated Vehicles.
  arXiv  Detail & Related papers  (2024-03-26T02:49:08Z)
• Safe Neural Control for Non-Affine Control Systems with Differentiable Control Barrier Functions [58.19198103790931]
  This paper addresses the problem of safety-critical control for non-affine control systems. It has been shown that optimizing quadratic costs subject to state and control constraints can be sub-optimally reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) We incorporate higher-order CBFs into neural ordinary differential equation-based learning models as differentiable CBFs to guarantee safety for non-affine control systems.
  arXiv  Detail & Related papers  (2023-09-06T05:35:48Z)
• Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations [50.37808220291108]
  This paper addresses learning safe output feedback control laws from partial observations of expert demonstrations. We first propose robust output control barrier functions (ROCBFs) as a means to guarantee safety. We then formulate an optimization problem to learn ROCBFs from expert demonstrations that exhibit safe system behavior.
  arXiv  Detail & Related papers  (2021-11-18T23:21:00Z)
• Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty [77.18483084440182]
  Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. We present a Gaussian Process (GP)-based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs.
  arXiv  Detail & Related papers  (2021-06-13T23:08:49Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions [96.63967125746747]
  Reinforcement learning framework learns the model uncertainty present in the CBF and CLF constraints. RL-CBF-CLF-QP addresses the problem of model uncertainty in the safety constraints.
  arXiv  Detail & Related papers  (2020-04-16T10:51:33Z)
• Learning Control Barrier Functions from Expert Demonstrations [69.23675822701357]
  We propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs) We analyze an optimization-based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz assumptions on the underlying dynamical system. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.
  arXiv  Detail & Related papers  (2020-04-07T12:29:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.