This paper studies safety guarantees for systems with time-varying control bounds. It has been shown that optimizing quadratic costs subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBFs). One of the main challenges in this method is that the CBF-based QP could easily become infeasible under tight control bounds, especially when the control bounds are time-varying. The recently proposed adaptive CBFs have addressed such infeasibility issues, but require extensive and non-trivial hyperparameter tuning for the CBF-based QP and may introduce overshooting control near the boundaries of safe sets. To address these issues, we propose a new type of adaptive CBFs called Auxiliary-Variable Adaptive CBFs (AVCBFs). Specifically, we introduce an auxiliary variable that multiplies each CBF itself, and define dynamics for the auxiliary variable to adapt it in constructing the corresponding CBF constraint. In this way, we can improve the feasibility of the CBF-based QP while avoiding extensive parameter tuning with non-overshooting control since the formulation is identical to classical CBF methods. We demonstrate the advantages of using AVCBFs and compare them with existing techniques on an Adaptive Cruise Control (ACC) problem with time-varying control bounds.

翻译：本文研究具有时变控制边界的系统安全保障问题。已有研究表明，利用控制屏障函数可将受状态和控制约束的二次成本优化问题简化为一系列二次规划。该方法的主要挑战在于，当控制边界较紧（尤其是时变控制边界）时，基于CBF的QP容易变得不可行。近期提出的自适应CBF解决了此类不可行性问题，但需要为基于CBF的QP进行大量且复杂的超参数调优，并可能在安全集边界附近引入超调控制。为解决这些问题，我们提出一种新型自适应CBF——辅助变量自适应CBF。具体而言，我们引入一个乘以每个CBF本身的辅助变量，并为其定义动力学方程以自适应地构建相应的CBF约束。这样，我们既能提高基于CBF的QP的可行性，又能避免大量参数调优，同时由于该公式与经典CBF方法一致，可实现无超调控制。我们通过具有时变控制边界的自适应巡航控制问题，展示了AVCBF的优势，并与现有技术进行了比较。