On Uniformly Time-Varying Control Barrier Functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915501364477952 |
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| author | Wiltz, Adrian Dimarogonas, Dimos V. |
| author_facet | Wiltz, Adrian Dimarogonas, Dimos V. |
| contents | This paper investigates the design of a subclass of time-varying Control Barrier Functions (CBFs), specifically that of uniformly time-varying CBFs. Leveraging the fact that CBFs encode a system's dynamic capabilities relative to a state constraint, we decouple the design of uniformly time-varying CBFs into a time-invariant and a time-varying component. We characterize the subclass of time-invariant CBFs that yield a uniformly time-varying CBF when combined with a specific type of time-varying function. A detailed analysis of those conditions under which the time-varying function preserves the CBF property of the time-invariant component is provided. These conditions allow for selecting the time-varying function such that diverse variations in the state constraints can be captured while avoiding the redesign of the time-invariant component. From a technical point of view, the analysis requires the derivation of novel relations for comparison functions, not previously reported in the literature. We further relax the requirements on the time-varying function, showing that forward invariance can still be ensured even when the uniformly time-varying value function does not strictly constitute a CBF. Finally, we discuss how existing CBF construction methods can be applied to design suitable time-invariant CBFs, and demonstrate the effectiveness of the approach through detailed numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Uniformly Time-Varying Control Barrier Functions Wiltz, Adrian Dimarogonas, Dimos V. Systems and Control Optimization and Control This paper investigates the design of a subclass of time-varying Control Barrier Functions (CBFs), specifically that of uniformly time-varying CBFs. Leveraging the fact that CBFs encode a system's dynamic capabilities relative to a state constraint, we decouple the design of uniformly time-varying CBFs into a time-invariant and a time-varying component. We characterize the subclass of time-invariant CBFs that yield a uniformly time-varying CBF when combined with a specific type of time-varying function. A detailed analysis of those conditions under which the time-varying function preserves the CBF property of the time-invariant component is provided. These conditions allow for selecting the time-varying function such that diverse variations in the state constraints can be captured while avoiding the redesign of the time-invariant component. From a technical point of view, the analysis requires the derivation of novel relations for comparison functions, not previously reported in the literature. We further relax the requirements on the time-varying function, showing that forward invariance can still be ensured even when the uniformly time-varying value function does not strictly constitute a CBF. Finally, we discuss how existing CBF construction methods can be applied to design suitable time-invariant CBFs, and demonstrate the effectiveness of the approach through detailed numerical examples. |
| title | On Uniformly Time-Varying Control Barrier Functions |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2509.15037 |