发表机构
Vanderbilt University（范德堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对半显式微分代数系统提出DAE感知控制障碍函数框架，通过投影向量场和SOS验证确保安全性与可行性，并在电力系统中验证。
AI 中文摘要
微分代数方程（DAE）系统出现在电力网络、多体力学和化学过程中，其中代数约束将动态状态与代数状态耦合。为常微分方程设计的标准控制障碍函数（CBF）方法在DAE系统中失效，因为代数约束施加的兼容性要求可能使安全过滤器不可行。本文针对半显式DAE系统，利用考虑与代数约束兼容性的CBF（称为DAE感知CBF）开发了一个安全关键控制框架。我们在约束流形上构造投影向量场以考虑隐藏动力学，同时确保保持代数约束满足的兼容性条件。随后，我们提出了平方和（SOS）验证条件，以证明所得DAE感知CBF的正确性和可行性。该框架在电力系统案例研究中得到验证。
英文摘要
Differential-algebraic equation (DAE) systems arise in power networks, multibody mechanics, and chemical processes, where algebraic constraints couple dynamic and algebraic states. Standard control barrier function (CBF) methods, designed for ordinary differential equations, fail for DAE systems because the algebraic constraints impose compatibility requirements that may render safety filters infeasible. This paper develops a safety-critical control framework for semi-explicit DAE systems using CBFs that consider compatibility with the algebraic constraints, termed DAE-aware CBFs. We construct projected vector fields on the constraint manifold to account for the hidden dynamics, while ensuring compatibility conditions that keep the algebraic constraints satisfied. We then present sum of squares (SOS) verification conditions that certify both correctness and feasibility of the resulting DAE-aware CBF. The framework is validated on power system case studies.
