Contraction-Guided Adaptive Partitioning for Reachability Analysis of Neural Network Controlled Systems
Contraction-Guided Adaptive Partitioning for Reachability Analysis of Neural Network Controlled Systems
复制标题
DOI：
10.1109/cdc49753.2023.10383360
复制
发表时间：
2023-04
期刊：
影响因子：
--
通讯作者：
Akash Harapanahalli;Saber Jafarpour;S. Coogan
中科院分区：
文献类型：
--
作者：
Akash Harapanahalli;Saber Jafarpour;S. Coogan
在本文中，我们提出了一个压缩引导的自适应分割算法，以改善区间值的鲁棒可达集估计的非线性反馈回路与神经网络控制器和干扰。基于对过度近似区间的收缩率的估计，该算法选择何时以及在何处进行划分。然后，通过利用神经网络验证步骤和可达性划分层的解耦，该算法可以以很小的计算成本提供精度改进。这种方法适用于任何足够精确的开环区间值可达性估计技术和任何限制神经网络输入输出行为的方法。使用基于收缩的鲁棒性分析，我们提供了具有混合单调可达性的算法性能保证。最后，我们证明了算法的性能，通过几个数值模拟，并将其与现有的方法在文献中。特别是，我们报告了一个相当大的改进，在一小部分的运行时可达集估计的准确性相比，国家的最先进的方法。
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate of the contraction rate of over-approximated intervals, the algorithm chooses when and where to partition. Then, by leveraging a decoupling of the neural network verification step and reachability partitioning layers, the algorithm can provide accuracy improvements for little computational cost. This approach is applicable with any sufficiently accurate open-loop interval-valued reachability estimation technique and any method for bounding the input-output behavior of a neural network. Using contraction-based robustness analysis, we provide guarantees of the algorithm's performance with mixed monotone reachability. Finally, we demonstrate the algorithm's performance through several numerical simulations and compare it with existing methods in the literature. In particular, we report a sizable improvement in the accuracy of reachable set estimation in a fraction of the runtime as compared to state-of-the-art methods.