# 基于 CBF 的安全滤波器在稳定平面线性系统中的吸引域

> 原文链接：https://robotics.hellobike.com/papers/2026-10-15-2610-21221
> 频道：papers | 更新日期：2026-10-15 | 标签：arxiv, cs.RO
> 核心摘要：研究CBF安全滤波器诱导的动力学，用平面线性系统参数刻画，并以车辆侧偏和三维示例说明。

# 基于 CBF 的安全滤波器在稳定平面线性系统中的吸引域

::: v-pre
> 原文链接：[Regions of Attraction of CBF-Based Safety Filters for Stable Planar Linear Systems](https://arxiv.org/abs/2610.21221)（arXiv 2610.21221 · 发布日期：2026-10-15）

**Regions of Attraction of CBF-Based Safety Filters for Stable Planar Linear Systems**

研究CBF安全滤波器诱导的动力学，用平面线性系统参数刻画，并以车辆侧偏和三维示例说明。

## 核心要点

- CBF安全滤波器通过最小修改名义控制器保证安全，但可能改变闭环动力学。
- 论文考虑平面线性对象、稳定线性名义控制器和仿射约束这一简单设置。
- 结果表明系统在保持安全时仍可能振荡或发散，并刻画原点全局稳定参数。
- 其他参数下约束边界出现鞍点；车辆侧偏和两个三维示例说明结果与变化。

**验证范围与局限**：验证范围为平面线性设置的理论刻画，并用车辆侧偏示例和两个三维示例说明。

## 英文摘要 (Abstract)

In this paper we study the dynamical properties induced by safety filters based on control barrier functions (CBFs). These are obtained by minimally modifying a nominal controller with the goal of rendering it safe. We consider the simple setting of a planar linear plant with a stable linear nominal controller and an affine constraint. We show that even in this simple setting, the filtered system can oscillate or diverge while remaining safe. We fully characterize the parameters for which the origin is globally (exponentially or asymptotically) stable. For all other parameters, the filter creates a saddle on the constraint boundary, and we characterize the region of attraction of the origin. For underdamped nominal dynamics, its boundary is an unstable periodic orbit, a homoclinic loop, or the saddle's stable manifold, depending on whether the CBF gain is below, at, or above a homoclinic transition value. A vehicle sideslip example and two three-dimensional examples illustrate the results and what changes beyond planar dynamics.

作者：Adam K. Kiss, Pol Mestres, András Bártfai, Shima Sadat Mousavi, Aaron Daniel Ames
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## 原始参考来源 (Sources)

- [arXiv 2610.21221：Regions of Attraction of CBF-Based Safety Filters for Stable Planar Linear Systems](https://arxiv.org/abs/2610.21221)