发表机构
University of California, Irvine; University of North Carolina at Chapel Hill（加州大学尔湾分校; 北卡罗来纳大学教堂山分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对控制障碍函数（CBF）仅能二元判定安全与否的局限，区分了内在与表示不可行性，提出与表示无关的安全度指标不变性权威需求（IAD），用于指导集合或执行器修复。
AI 中文摘要
有效的控制障碍函数（CBF）可证明其表示的安全集能被实现为前向不变集，其取值符号可指示状态是否安全，但无法量化二元指示之外的安全度。本文证明，在表示同一安全集的有效CBF中，内部值和梯度可任意改变，因此二者均无法确定独立于集合表示方式的安全度；还证明基于候选CBF的不等式约束是否可行本身无法量化安全度，具体而言，不可行可能源于安全集不具备控制不变性，也可能源于候选CBF表示失效，这促使我们区分内在不可行性与表示不可行性。最后，我们引入不变性权威需求（IAD），这是一种与表示无关的安全度，可量化控制不变性所需的控制权威，用于指导集合或执行器的修复。
英文摘要
A valid control barrier function (CBF) certifies if its represented safe set can be rendered forward invariant, and the sign of its value indicates whether a state is safe or not, but it does not quantify a degree of safety beyond the binary indication. In this paper, we show that among valid CBFs representing the same safe set, interior values and gradients can be changed arbitrarily, so neither quantity determines a degree of safety that is independent of how the set is represented. We also show that whether a candidate CBF-based inequality constraint is feasible does not by itself quantify a degree of safety. In particular, infeasibility can occur either because the safe set is not controlled invariant or because the candidate CBF representation fails. This motivates our distinction between intrinsic and representational infeasibility. Finally, we introduce the invariance authority demand (IAD), a representation-independent degree of safety that quantifies the control authority required for controlled invariance and can be used to guide set or actuator repair.
