{"ID":2893311,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.12743","arxiv_id":"2507.12743","title":"Invariance Guarantees using Continuously Parametrized Control Barrier Functions","abstract":"Constructing a control invariant set with an appropriate shape that fits within a given state constraint is a fundamental problem in safety-critical control but is known to be difficult, especially for large or complex spaces. This paper introduces a safe control framework of utilizing PCBF: continuously parametrized control barrier functions (CBFs). In PCBF, each choice of parameter corresponds to a control invariant set of relatively simple shape. Invariance-preserving control is done by dynamically selecting a parameter whose corresponding invariant set lies within the safety bound. This eliminates the need for synthesizing a single complex CBF that matches the entire free space. It also enables easier adaptation to diverse environments. By assigning a differentiable dynamics on the parameter space, we derive a lightweight feedback controller based on quadratic programming (QP), namely PCBF-QP. We also discuss on how to build a valid PCBF for a class of systems and how to constrain the parameter so that the invariant set does not exceed the safety bound. The concept is also extended to cover continuously parametrized high-order CBFs, which is called high-order PCBF. Finally, simulation experiments are conducted to validate the proposed approach.","short_abstract":"Constructing a control invariant set with an appropriate shape that fits within a given state constraint is a fundamental problem in safety-critical control but is known to be difficult, especially for large or complex spaces. This paper introduces a safe control framework of utilizing PCBF: continuously parametrized c...","url_abs":"https://arxiv.org/abs/2507.12743","url_pdf":"https://arxiv.org/pdf/2507.12743v1","authors":"[\"Inkyu Jang\",\"H. Jin Kim\"]","published":"2025-07-17T02:56:05Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}