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.

本研究提出了一种基于收缩率指导的自适应分区算法，用于改进非线性反馈环路中神经网络控制器及干扰对区间值可靠范围估计的影响。该算法利用对上估计间隔的收缩率的估计结果，在选定时间和位置进行分区，并通过神经网络验证步骤和可达性分区层的分离，以小的计算成本提供准确性改进。使用基于收缩的稳健性分析，我们提供了混合单调到达性的算法性能保证。最后，通过几个数值模拟和与文献中现有方法的比较，证明了算法的性能表现，特别是在低运行时时间的情况下提高了到达集的估计精度。

神经网络控制系统可达性分析中的收缩引导自适应划分