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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2507.12717 |
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| _version_ | 1866909692474687488 |
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| author | Ong, Pio Cohen, Max H. Molnar, Tamas G. Ames, Aaron D. |
| author_facet | Ong, Pio Cohen, Max H. Molnar, Tamas G. Ames, Aaron D. |
| contents | Control barrier functions provide a powerful means for synthesizing safety filters that ensure safety framed as forward set invariance. Key to CBFs' effectiveness is the simple inequality on the system dynamics: $\dot{h} \geq - α(h)$. Yet determining the class $\mathcal{K}^e$ function $α$ is a user defined choice that can have a dramatic effect on the resulting system behavior. This paper formalizes the process of choosing $α$ using optimal-decay control barrier functions (OD-CBFs). These modify the traditional CBF inequality to: $\dot{h} \geq - ωα(h)$, where $ω\geq 0$ is automatically determined by the safety filter. A comprehensive characterization of this framework is elaborated, including tractable conditions on OD-CBF validity, control invariance of the underlying sets in the state space, forward invariance conditions for safe sets, and discussion on optimization-based safe controllers in terms of their feasibility, Lipschitz continuity, and closed-form expressions. The framework also extends existing higher-order CBF techniques, addressing safety constraints with vanishing relative degrees. The proposed method is demonstrated on a satellite control problem in simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Properties of Optimal-Decay Control Barrier Functions Ong, Pio Cohen, Max H. Molnar, Tamas G. Ames, Aaron D. Systems and Control Control barrier functions provide a powerful means for synthesizing safety filters that ensure safety framed as forward set invariance. Key to CBFs' effectiveness is the simple inequality on the system dynamics: $\dot{h} \geq - α(h)$. Yet determining the class $\mathcal{K}^e$ function $α$ is a user defined choice that can have a dramatic effect on the resulting system behavior. This paper formalizes the process of choosing $α$ using optimal-decay control barrier functions (OD-CBFs). These modify the traditional CBF inequality to: $\dot{h} \geq - ωα(h)$, where $ω\geq 0$ is automatically determined by the safety filter. A comprehensive characterization of this framework is elaborated, including tractable conditions on OD-CBF validity, control invariance of the underlying sets in the state space, forward invariance conditions for safe sets, and discussion on optimization-based safe controllers in terms of their feasibility, Lipschitz continuity, and closed-form expressions. The framework also extends existing higher-order CBF techniques, addressing safety constraints with vanishing relative degrees. The proposed method is demonstrated on a satellite control problem in simulation. |
| title | On the Properties of Optimal-Decay Control Barrier Functions |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2507.12717 |