mlsanityData to 14 Oct 2026

Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions

arXiv 2208.10733 ↗First posted 23 Aug 2022eess.SY cs.LG cs.SYcited by 2

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Abstract (arXiv)

Learning-based control has recently shown great efficacy in performing complex tasks for various applications. However, to deploy it in real systems, it is of vital importance to guarantee the system will stay safe. Control Barrier Functions (CBFs) offer mathematical tools for designing safety-preserving controllers for systems with known dynamics. In this article, we first introduce a model-uncertainty-aware reformulation of CBF-based safety-critical controllers using Gaussian Process (GP) regression to close the gap between an approximate mathematical model and the real system, which results in a second-order cone program (SOCP)-based control design. We then present the pointwise feasibility conditions of the resulting safety controller, highlighting the level of richness that the available system information must meet to ensure safety. We use these conditions to devise an event-triggered online data collection strategy that ensures the recursive feasibility of the learned safety controller. Our method works by constantly reasoning about whether the current information is sufficient to ensure safety or if new measurements under active safe exploration are required to reduce the uncertainty. As a result, our proposed framework can guarantee the forward invariance of the safe set defined by the CBF with high probability, even if it contains a priori unexplored regions. We validate the proposed framework in two numerical simulation experiments.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 37 of its 66 references that are in the map. First posted on arXiv 23 Aug 2022.

Builds on

37 of 66 references.

References · 37

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25 more
  1. 2016Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processescited by 39
  2. 2020Neural Certificates for Safe Control Policiescited by 35
  3. 2020Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functionscited by 33
  4. 2016Robustness of Control Barrier Functions for Safety Critical Controlcited by 30
  5. 2019Adaptive Safety with Control Barrier Functionscited by 25
  6. 2019Feedback Linearization based on Gaussian Processes with event-triggered Online Learningcited by 24
  7. 2020Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertaintiescited by 20
  8. 2020Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processescited by 20
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  17. 2021Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertaintycited by 13
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  20. 2021Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functionscited by 11
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Cited by year

Citing papers per year: 2023: 2.

2 papers.

  1. 2023Can Learning Deteriorate Control? Analyzing Computational Delays in Gaussian Process-Based Event-Triggered Online Learningcited by 8
  2. 2023Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learningcited by 1