Characterizing Safety: Minimal Barrier Functions from Scalar Comparison Systems
Characterizing Safety: Minimal Barrier Functions from Scalar Comparison Systems
复制标题
表征安全性：标量比较系统的最小障碍函数
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
S. Coogan
中科院分区：
文献类型：
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作者：
Rohit Konda;A. Ames;S. Coogan
验证集不变性的经典解源于Nagumo的开创性工作，并通过光滑障碍函数约束不等式定义集合，从而得到保证集不变性的可计算流动条件。虽然这些关于集不变性的历史结果大多考虑了边界上的流动条件，但最近关于控制障碍函数的结果将这些条件扩展到整个集合，尽管它们要求障碍函数的正则性条件。通过直接利用比较结果来定义系统整个区域上的流动条件，通过最小障碍函数来充分刻画集合的不变性。这种方法的一个相当大的好处是去掉了屏障函数的正则性假设。本文还给出了一个有效的微分不等式条件的充要条件，给出了这类方法的最小条件。我们还证明了什么时候极小障碍函数是集合不变性的充要条件。
Verifying set invariance has classical solutions stemming from the seminal work by Nagumo, and defining sets via a smooth barrier function constraint inequality results in computable flow conditions for guaranteeing set invariance. While a majority of these historic results on set invariance consider flow conditions on the boundary, recent results on control barrier functions extended these conditions to the entire set, although they required regularity conditions on the barrier function. This paper fully characterizes set invariance through \emph{minimal barrier functions} by directly appealing to a comparison result to define a flow condition over the entire domain of the system. A considerable benefit of this approach is the removal of regularity assumptions of the barrier function. This paper also outlines necessary and sufficient conditions for a valid differential inequality condition, giving the minimum conditions for this type of approach. We also show when minimal barrier functions are necessary and sufficient for set invariance.
影响因子：
6.4
作者：
Maghenem, Mohamed;Sanfelice, Ricardo G.
通讯作者：
Sanfelice, Ricardo G.