为随机控制系统的安全约束设计可验证的神经屏障函数方法
Stochastic Neural Control Barrier Functions
- 提出无验证的平滑神经屏障函数合成框架
- 针对带ReLU的神经屏障函数设计闭环验证合成方案
- 在三类系统上验证了方法的有效性与安全性
控制屏障函数（CBFs）用于保障控制系统安全性，作为不损害性能的安全过滤器。其有效性依赖于有效CBF的构造。由于复杂性，可由神经网络表示，称为神经控制屏障函数（NCBFs）。现有工作集中于确定性环境下的NCBF合成与验证，对随机情形下的神经屏障函数（SNCBFs）研究不足。本文提出可验证安全的SNCBF合成方法，涵盖具有二阶可微激活函数的平滑情况，以及使用ReLU激活函数的情形。针对平滑SNCBFs，提出无需验证的合成框架；针对平滑与ReLU型SNCBFs，提出验证闭环的合成框架。在倒立摆、Darboux模型和单轮车模型三个系统中进行了验证。
原文摘要 · Abstract (English)
Control Barrier Functions (CBFs) are utilized to ensure the safety of control systems. CBFs act as safety filters in order to provide safety guarantees without compromising system performance. These safety guarantees rely on the construction of valid CBFs. Due to their complexity, CBFs can be represented by neural networks, known as neural CBFs (NCBFs). Existing works on the verification of the NCBF focus on the synthesis and verification of NCBFs in deterministic settings, leaving the stochastic NCBFs (SNCBFs) less studied. In this work, we propose a verifiably safe synthesis for SNCBFs. We consider the cases of smooth SNCBFs with twice-differentiable activation functions and SNCBFs that utilize the Rectified Linear Unit or ReLU activation function. We propose a verification-free synthesis framework for smooth SNCBFs and a verification-in-the-loop synthesis framework for both smooth and ReLU SNCBFs. and we validate our frameworks in three cases, namely, the inverted pendulum, Darboux, and the unicycle model.
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