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arXiv · 2507.12743

Invariance Guarantees using Continuously Parametrized Control Barrier Functions

Inkyu Jang·H. Jin Kim
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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.

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BibTeXRIS

Inkyu Jang, H. Jin Kim. 2025-07-17. Invariance Guarantees using Continuously Parametrized Control Barrier Functions. https://arxiv.org/abs/2507.12743

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