标题： 关于控制屏障函数的最优性、稳定性和可行性：基于自适应学习的方法 显示英文标题

标题： On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach

摘要： 安全问题一直是基于学习的方法在现实世界应用部署中的关键问题。为了解决这个问题，控制屏障函数（CBF）及其变体在安全性至关重要的控制中引起了广泛关注。然而，由于CBF具有短视的一步特性，并且缺乏设计类-$\mathcal{K}$函数的原则性方法，当前CBF仍然存在一些根本性的局限性：最优性、稳定性以及可行性。本文提出了一种新颖且统一的方法，即自适应多步控制屏障函数（AM-CBF），通过神经网络参数化类-$\mathcal{K}$函数，并与强化学习策略一起训练，以解决这些局限性。此外，为了缓解CBF的短视特性，我们提出了一种新颖的\textit{多步训练和单步执行}范式，使CBF具有远见性，同时执行时仍只需求解单步凸二次规划。我们的方法在各种场景下的第一和第二阶系统中进行了评估，实验结果显示我们的方法在定性和定量上都优于传统的CBF。 显示英文摘要

摘要： Safety has been a critical issue for the deployment of learning-based approaches in real-world applications. To address this issue, control barrier function (CBF) and its variants have attracted extensive attention for safety-critical control. However, due to the myopic one-step nature of CBF and the lack of principled methods to design the class-$\mathcal{K}$ functions, there are still fundamental limitations of current CBFs: optimality, stability, and feasibility. In this paper, we proposed a novel and unified approach to address these limitations with Adaptive Multi-step Control Barrier Function (AM-CBF), where we parameterize the class-$\mathcal{K}$ function by a neural network and train it together with the reinforcement learning policy. Moreover, to mitigate the myopic nature, we propose a novel \textit{multi-step training and single-step execution} paradigm to make CBF farsighted while the execution remains solving a single-step convex quadratic program. Our method is evaluated on the first and second-order systems in various scenarios, where our approach outperforms the conventional CBF both qualitatively and quantitatively.