From Time-Invariant to Uniformly Time-Varying Control Barrier Functions: A Constructive Approach
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917756398469120 |
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| author | Wiltz, Adrian Dimarogonas, Dimos V. |
| author_facet | Wiltz, Adrian Dimarogonas, Dimos V. |
| contents | In this paper, we define and analyze a subclass of (time-invariant) Control Barrier Functions (CBF) that have favorable properties for the construction of uniformly timevarying CBFs and thereby for the satisfaction of uniformly time-varying constraints. We call them Λ-shiftable CBFs where Λ states the extent by which the CBF can be varied by adding a time-varying function. Moreover, we derive sufficient conditions under which a time-varying CBF can be obtained from a time-invariant one, and we propose a systematic construction method. Advantageous about our approach is that a Λ-shiftable CBF, once constructed, can be reused for various control objectives. In the end, we relate the class of Λ-shiftable CBFs to Control Lyapunov Functions (CLF), and we illustrate the application of our results with a relevant simulation example. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_12964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From Time-Invariant to Uniformly Time-Varying Control Barrier Functions: A Constructive Approach Wiltz, Adrian Dimarogonas, Dimos V. Systems and Control In this paper, we define and analyze a subclass of (time-invariant) Control Barrier Functions (CBF) that have favorable properties for the construction of uniformly timevarying CBFs and thereby for the satisfaction of uniformly time-varying constraints. We call them Λ-shiftable CBFs where Λ states the extent by which the CBF can be varied by adding a time-varying function. Moreover, we derive sufficient conditions under which a time-varying CBF can be obtained from a time-invariant one, and we propose a systematic construction method. Advantageous about our approach is that a Λ-shiftable CBF, once constructed, can be reused for various control objectives. In the end, we relate the class of Λ-shiftable CBFs to Control Lyapunov Functions (CLF), and we illustrate the application of our results with a relevant simulation example. |
| title | From Time-Invariant to Uniformly Time-Varying Control Barrier Functions: A Constructive Approach |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2408.12964 |