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：本文研究了具有时变控制约束系统的安全保证问题。已有研究表明，在状态和控制约束下优化二次成本可转化为使用控制障碍函数（CBF）的一系列二次规划（QP）。该方法的主要挑战之一是，在严格的控制约束下（尤其是当控制约束为时变时），基于CBF的QP很容易变得不可行。最近提出的自适应CBF解决了这种不可行性问题，但需要对基于CBF的QP进行大量且非平凡的超参数调整，并且可能在安全集边界附近引入超调控制。为了解决这些问题，我们提出了一种新型自适应CBF，称为辅助变量自适应CBF（AVCBF）。具体而言，我们引入一个辅助变量乘以每个CBF自身，并为该辅助变量定义动力学以自适应地构造相应的CBF约束。通过这种方式，我们可以在避免大量参数调整且不产生超调控制的情况下提高基于CBF的QP的可行性——因为其公式与经典CBF方法相同。我们通过一个具有时变控制约束的自适应巡航控制（ACC）问题，展示了AVCBF的优势，并与现有技术进行了比较。