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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12885 |
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| _version_ | 1866918295237558272 |
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| author | Mousavi, Shima Sadat Tan, Xiao Ames, Aaron D. |
| author_facet | Mousavi, Shima Sadat Tan, Xiao Ames, Aaron D. |
| contents | This paper develops certificates that propagate compatibility of multiple control barrier function (CBF) constraints from sampled vertices to their convex hull. Under mild concavity and affinity assumptions, we present three sufficient feasibility conditions under which feasible inputs over the convex hull can be obtained per coordinate, with a common input, or via convex blending. We also describe the associated computational methods, based on interval intersections or an offline linear program (LP). Beyond certifying compatibility, we give conditions under which the quadratic-program (QP) safety filter is affine in the state. This enables explicit implementations via convex combinations of vertex-feasible inputs. Case studies illustrate the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12885 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Vertices to Convex Hulls: Certifying Set-Wise Compatibility for CBF Constraints Mousavi, Shima Sadat Tan, Xiao Ames, Aaron D. Systems and Control This paper develops certificates that propagate compatibility of multiple control barrier function (CBF) constraints from sampled vertices to their convex hull. Under mild concavity and affinity assumptions, we present three sufficient feasibility conditions under which feasible inputs over the convex hull can be obtained per coordinate, with a common input, or via convex blending. We also describe the associated computational methods, based on interval intersections or an offline linear program (LP). Beyond certifying compatibility, we give conditions under which the quadratic-program (QP) safety filter is affine in the state. This enables explicit implementations via convex combinations of vertex-feasible inputs. Case studies illustrate the results. |
| title | From Vertices to Convex Hulls: Certifying Set-Wise Compatibility for CBF Constraints |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2601.12885 |