CPED-NCBFs：一种基于专家演示的神经控制屏障函数的共形预测方法
CPED-NCBFs: A Conformal Prediction for Expert Demonstration-based Neural Control Barrier Functions
AI总结：
本文提出CPED-NCBFs方法，利用分裂共形预测验证从专家演示中学习到的神经控制屏障函数，并在质点系统和独轮车模型上验证了其有效性。
摘要：
在控制系统中实现安全性的诸多有前景的方法中，从专家演示中学习控制屏障函数（CBFs）已成为一种有效策略。然而，一个关键挑战仍然存在：验证学习到的CBFs是否能在整个状态空间中真正保证安全性。当CBF使用神经网络表示（NCBFs）时，这一问题尤为困难。现有的几种验证技术试图解决该问题，包括基于SMT的求解器、混合整数规划（MIP）以及区间或边界传播方法，但这些方法往往引入宽松且保守的边界。为克服这些局限性，本文使用CPED-NCBFs——一种基于分裂共形预测的验证策略——来验证从专家演示中学习到的NCBF。我们进一步在质点系统和独轮车模型上验证了所提方法，以证明所提理论的有效性。
英文摘要：
Among the promising approaches to enforce safety in control systems, learning Control Barrier Functions (CBFs) from expert demonstrations has emerged as an effective strategy. However, a critical challenge remains: verifying that the learned CBFs truly enforce safety across the entire state space. This is especially difficult when CBF is represented using neural networks (NCBFs). Several existing verification techniques attempt to address this problem including SMT-based solvers, mixed-integer programming (MIP), and interval or bound-propagation methods but these approaches often introduce loose, conservative bounds. To overcome these limitations, in this work we use CPED-NCBFs a split-conformal prediction based verification strategy to verify the learned NCBF from the expert demonstrations. We further validate our method on point mass systems and unicycle models to demonstrate the effectiveness of the proposed theory.
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