基于极限学习机的障碍函数综合
Fast and Sample Efficient Safety Verification via Extreme Learning Machine
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- Indian Institute of Science, Bengaluru, India（印度科学学院）
- Technical University of Munich, Germany（慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。
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中文总结 AI 辅助
针对未知离散时间系统的安全验证，提出基于极限学习机的障碍证书综合方法，利用其架构简单和凸优化特性提升收敛与计算效率，并通过最小化Lipschitz常数和网格采样实现形式验证。
中文摘要 AI 辅助
深度学习如神经网络等方法极大地简化了具有未知动力学的复杂非线性系统安全证书的计算。然而，由于这些证书的数据驱动特性以及神经网络的复杂架构，计算时间以及跨未见数据的鲁棒性保证仍然是一个挑战。本工作旨在通过综合基于极限学习机（ELM）的障碍证书，正式验证离散时间未知系统的安全属性。与神经网络对应方法相比，该方法因其架构简单和底层优化问题的凸性，大大提高了收敛保证并缩短了计算时间。通过最小化候选障碍的Lipschitz常数，我们提出了一种基于网格的采样技术，以使用所需的最小样本数正式验证其有效性。我们通过数值示例展示了我们方法的有效性，并与传统的基于深度学习的证书综合方法进行比较，以突出其优势。
英文摘要
Deep learning methods like neural networks have greatly simplified the computation of safety certificates for complex nonlinear systems with unknown dynamics. However, due to the data-driven nature of these certificates and the complex architecture of neural networks, computation time as well as robustness guarantees across unseen data remain a challenge. This work aims to formally verify safety properties of discrete-time unknown systems by synthesizing extreme learning machine (ELM)-based barrier certificates. Compared to neural network counterparts, this approach greatly improves convergence guarantees and computational time due to its architectural simplicity and the convex nature of the underlying optimization problem. By minimizing the Lipschitz constant of the candidate barrier, we present a grid-based sampling technique to formally verify its validity using the minimum number of samples required. We demonstrate through numerical examples the effectiveness of our approach, and compare with traditional deep-learning based certificate synthesis to highlight its benefits.
