用正性结构实现神经网络控制的延迟无关安全验证
Delay Independent Safe Control with Neural Networks: Positive Lur'e Certificates for Risk Aware Autonomy
- 基于局部扇形界与正性结构构建延迟无关稳定性证书
- 验证速度比传统SDP方法快数个数量级，且覆盖更广不确定区间
- 适合需要高实时性与风险敏感控制的自主系统场景
本文提出一种面向自主学习型控制系统的风险感知安全认证方法。针对状态/输入延迟和区间矩阵不确定性两类现实风险，将神经网络控制器建模为局部扇形边界，并利用正性结构推导出线性、延迟无关的稳定性证书，可在可接受的不确定性范围内保证局部指数稳定。为评估性能，采用并实现了最先进的IQCs神经网络验证流程。在典型测试案例中，基于正性的验证方法运行速度比基于SDP的IQC方法快数个数量级，且能认证出后者无法覆盖的控制区域，提供了可扩展的安全保障，有效补充了风险敏感控制需求。
原文摘要 · Abstract (English)
We present a risk-aware safety certification method for autonomous, learning enabled control systems. Focusing on two realistic risks, state/input delays and interval matrix uncertainty, we model the neural network (NN) controller with local sector bounds and exploit positivity structure to derive linear, delay-independent certificates that guarantee local exponential stability across admissible uncertainties. To benchmark performance, we adopt and implement a state-of-the-art IQC NN verification pipeline. On representative cases, our positivity-based tests run orders of magnitude faster than SDP-based IQC while certifying regimes the latter cannot-providing scalable safety guarantees that complement risk-aware control.
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