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.

翻译：本文提出了一种基于收缩引导的自适应分区算法，旨在改进含神经网络控制器和扰动的非线性反馈回路中区间值鲁棒可达集估计。该算法根据超近似区间的收缩率估计值，自主选择分区时机和位置；通过解耦神经网络验证步骤与可达性分区层，能够在较低计算成本下提升估计精度。该方法适用于任意足够精确的开环区间值可达性估计技术，以及任意神经网络输入输出行为边界约束方法。基于收缩鲁棒性分析，我们利用混合单调可达性理论证明了算法的性能保障。最后通过数值仿真验证算法性能，并与现有文献方法进行对比。特别地，与现有最先进方法相比，本算法在显著缩短运行时间的同时，实现了可达集估计精度的大幅提升。