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 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界限系统的安全保障问题。已有研究表明，通过使用控制屏障函数（CBFs），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（QPs）。该方法的主要挑战之一是：在紧控制界限（尤其是时变控制界限）下，基于CBF的QP可能极易变得不可行。最近提出的自适应CBFs虽解决了此类不可行性问题，但需要对基于CBF的QP进行广泛且非平凡的的超参数调优，并可能在安全集边界附近引发控制超调。为解决这些问题，我们提出一种新型自适应CBFs——辅助变量控制屏障函数（AVCBFs）。具体而言，我们引入一个乘以每个CBF自身的辅助变量，并定义该辅助变量的动态特性以自适应构建相应的CBF约束。通过这种方式，我们能在避免广泛参数调优的同时改善基于CBF的QP的可行性，且由于公式化过程与经典CBF方法相同，可实现无超调控制。我们通过具有时变控制界限的自适应巡航控制（ACC）问题，展示了AVCBFs的优势，并与现有技术进行了对比。