mlsanityData to 7 Oct 2026

Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty

arXiv 2106.07108 ↗First posted 13 Jun 2021eess.SY cs.LG cs.SYcited by 13

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Abstract (arXiv)

Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. They are commonly utilized to build constraints that can be incorporated in a min-norm quadratic program (CBF-CLF-QP) which solves for a safety-critical control input. However, since these constraints rely on a model of the system, when this model is inaccurate the guarantees of safety and stability can be easily lost. In this paper, we present a Gaussian Process (GP)-based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs. The considered model uncertainty is affected by both state and control input. We derive probabilistic bounds on the effects that such model uncertainty has on the dynamics of the CBF and CLF. We then use these bounds to build safety and stability chance constraints that can be incorporated in a min-norm convex optimization-based controller, called GP-CBF-CLF-SOCP. As the main theoretical result of the paper, we present necessary and sufficient conditions for pointwise feasibility of the proposed optimization problem. We believe that these conditions could serve as a starting point towards understanding what are the minimal requirements on the distribution of data collected from the real system in order to guarantee safety. Finally, we validate the proposed framework with numerical simulations of an adaptive cruise controller for an automotive system.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 13 of its 25 references that are in the map. First posted on arXiv 13 Jun 2021.

Builds on

13 of 25 references.

References · 13

  1. 2019Control Barrier Functions: Theory and Applicationscited by 332
  2. 2019Learning for Safety-Critical Control with Control Barrier Functionscited by 66
  3. 2020Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functionscited by 61
  4. 2016Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processescited by 38
  5. 2018Data-Enabled Predictive Control: In the Shallows of the DeePCcited by 33
  6. 2019Adaptive Safety with Control Barrier Functionscited by 25
  7. 2020Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertaintiescited by 20
  8. 2019Bayesian Learning-Based Adaptive Control for Safety Critical Systemscited by 19
  9. 2020Control Barriers in Bayesian Learning of System Dynamicscited by 17
  10. 2020Towards Robust Data-Driven Control Synthesis for Nonlinear Systems with Actuation Uncertaintycited by 13
  11. 2020Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamicscited by 12
  12. 2020The Impact of Data on the Stability of Learning-Based Control- Extended Versioncited by 6
1 more
  1. 2020Learning Min-norm Stabilizing Control Laws for Systems with Unknown Dynamicscited by 4

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Citing papers per year: 2021: 2; 2022: 3; 2023: 4; 2024: 4.

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  1. 2022SABLAS: Learning Safe Control for Black-box Dynamical Systemscited by 17
  2. 2023In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution Statescited by 15
  3. 2023Distributionally Robust Statistical Verification with Imprecise Neural Networkscited by 12
  4. 2022End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functionscited by 10
  5. 2024Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanescited by 8
  6. 2024Random Features Approximation for Control-Affine Systemscited by 3
  7. 2024DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safetycited by 3
  8. 2022Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functionscited by 2
  9. 2021Safety-Critical Learning of Robot Control with Temporal Logic Specificationscited by 1
  10. 2023Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learningcited by 1
  11. 2024Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Modelscited by 1
  12. 2021ProBF: Learning Probabilistic Safety Certificates with Barrier Functionscited by 0
1 more
  1. 2023Safe Online Dynamics Learning with Initially Unknown Models and Infeasible Safety Certificatescited by 0