mlsanityData to 14 Oct 2026

On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach

arXiv 2305.03608 ↗First posted 5 May 2023cs.LG cs.RO cs.SYcited by 4

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Abstract (arXiv)

Safety has been a critical issue for the deployment of learning-based approaches in real-world applications. To address this issue, control barrier function (CBF) and its variants have attracted extensive attention for safety-critical control. However, due to the myopic one-step nature of CBF and the lack of principled methods to design the class-K functions, there are still fundamental limitations of current CBFs: optimality, stability, and feasibility. In this paper, we proposed a novel and unified approach to address these limitations with Adaptive Multi-step Control Barrier Function (AM-CBF), where we parameterize the class-K function by a neural network and train it together with the reinforcement learning policy. Moreover, to mitigate the myopic nature, we propose a novel textitmulti-step training and single-step execution paradigm to make CBF farsighted while the execution remains solving a single-step convex quadratic program. Our method is evaluated on the first and second-order systems in various scenarios, where our approach outperforms the conventional CBF both qualitatively and quantitatively.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 22 of its 35 references that are in the map. First posted on arXiv 5 May 2023.

Builds on

22 of 35 references.

References · 22

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10 more
  1. 2020Safe Reinforcement Learning via Curriculum Inductioncited by 74
  2. 2019Differentiating Through a Cone Programcited by 73
  3. 2020Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functionscited by 68
  4. 2021Safe Reinforcement Learning Using Robust Control Barrier Functionscited by 59
  5. 2020Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approachcited by 23
  6. 2021Predictive control barrier functions: Enhanced safety mechanisms for learning-based controlcited by 14
  7. 2021Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approachcited by 13
  8. 2020Safe Reinforcement Learning of Control-Affine Systems with Vertex Networkscited by 8
  9. 2020Sufficient Conditions for Feasibility of Optimal Control Problems Using Control Barrier Functionscited by 7
  10. 2021A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stabilitycited by 6

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Cited by year

Citing papers per year: 2023: 1; 2024: 0; 2025: 3.

4 papers.

  1. 2025Certificated Actor-Critic: Hierarchical Reinforcement Learning with Control Barrier Functions for Safe Navigationcited by 2
  2. 2023Distributionally Safe Reinforcement Learning under Model Uncertainty: A Single-Level Approach by Differentiable Convex Programmingcited by 1
  3. 2025Safe Learning Control with Optimality and Stability Guaranteescited by 1
  4. 2025Safe model-based Reinforcement Learning via Model Predictive Control and Control Barrier Functionscited by 1