Sampling-Aware Control Barrier Functions for Safety-Critical and Finite-Time Constrained Control
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910109877141504 |
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| author | Liu, Shuo Xiao, Wei Belta, Calin A. |
| author_facet | Liu, Shuo Xiao, Wei Belta, Calin A. |
| contents | In safety-critical control systems, ensuring both safety and feasibility under sampled-data implementations is crucial for practical deployment. Existing Control Barrier Function (CBF) frameworks, such as High-Order CBFs (HOCBFs), effectively guarantee safety in continuous time but may become unsafe when executed under zero-order-hold (ZOH) controllers due to inter-sampling effects. Moreover, they do not explicitly handle finite-time reach-and-remain requirements or multiple simultaneous constraints, which often lead to conflicts between safety and reach-and-remain objectives, resulting in feasibility issues during control synthesis. This paper introduces Sampling-Aware Control Barrier Functions (SACBFs), a unified framework that accounts for sampling effects and high relative-degree constraints by estimating and incorporating Taylor-based upper bounds on barrier evolution between sampling instants. The proposed method guarantees continuous-time forward invariance of safety and finite-time reach-and-remain sets under ZOH control. To further improve feasibility, a relaxed variant (r-SACBF) introduces slack variables for handling multiple constraints realized through time-varying CBFs. Simulation studies on a unicycle robot demonstrate that SACBFs achieve safe and feasible performance in scenarios where traditional HOCBF methods fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sampling-Aware Control Barrier Functions for Safety-Critical and Finite-Time Constrained Control Liu, Shuo Xiao, Wei Belta, Calin A. Systems and Control In safety-critical control systems, ensuring both safety and feasibility under sampled-data implementations is crucial for practical deployment. Existing Control Barrier Function (CBF) frameworks, such as High-Order CBFs (HOCBFs), effectively guarantee safety in continuous time but may become unsafe when executed under zero-order-hold (ZOH) controllers due to inter-sampling effects. Moreover, they do not explicitly handle finite-time reach-and-remain requirements or multiple simultaneous constraints, which often lead to conflicts between safety and reach-and-remain objectives, resulting in feasibility issues during control synthesis. This paper introduces Sampling-Aware Control Barrier Functions (SACBFs), a unified framework that accounts for sampling effects and high relative-degree constraints by estimating and incorporating Taylor-based upper bounds on barrier evolution between sampling instants. The proposed method guarantees continuous-time forward invariance of safety and finite-time reach-and-remain sets under ZOH control. To further improve feasibility, a relaxed variant (r-SACBF) introduces slack variables for handling multiple constraints realized through time-varying CBFs. Simulation studies on a unicycle robot demonstrate that SACBFs achieve safe and feasible performance in scenarios where traditional HOCBF methods fail. |
| title | Sampling-Aware Control Barrier Functions for Safety-Critical and Finite-Time Constrained Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2511.11897 |