用分块方法验证神经网络控制器的系统稳定性
Verifying Closed-Loop Contractivity of Learning-Based Controllers via Partitioning
- 通过区间分析构建可计算的稳定判据
- 在倒立摆系统上实现可证明稳定的神经控制
- 适合关注控制系统安全性的研究者
针对控制器和收缩度量均由神经网络参数化的非线性控制系统，本文提出一种验证闭环收缩性的方法。利用区间分析与区间边界传播，推导出一个可计算且可扩展的充分条件，该条件等价于检查一个对称梅茨勒矩阵的主特征值非正。将此充分条件与域分块策略结合，嵌入训练过程。在倒立摆系统上的实验表明，所提方法能学习到满足收缩性条件的神经网络控制器与收缩度量，实现可证明的系统稳定性。
原文摘要 · Abstract (English)
We address the problem of verifying closed-loop contraction in nonlinear control systems whose controller and contraction metric are both parameterized by neural networks. By leveraging interval analysis and interval bound propagation, we derive a tractable and scalable sufficient condition for closed-loop contractivity that reduces to checking that the dominant eigenvalue of a symmetric Metzler matrix is nonpositive. We combine this sufficient condition with a domain partitioning strategy to integrate this sufficient condition into training. The proposed approach is validated on an inverted pendulum system, demonstrating the ability to learn neural network controllers and contraction metrics that provably satisfy the contraction condition.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。