非线性网络的流收缩证书：部分观测下的拓扑感知数据充分性
Streaming Contraction Certificates for Nonlinear Networks: Topology-Aware Data Sufficiency with Partial Observation
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中文总结 AI 辅助
针对现有框架无法实时从非线性互联系统部分观测认证控制动作安全性的问题，本文开发流收缩证书，并引入拓扑感知估计器，在五节点非线性基准测试中取得良好效果，适用于大规模非线性网络系统。
中文摘要 AI 辅助
实时从非线性互联系统的流部分观测中，在非平稳干扰下认证控制动作的安全性，是现有数据驱动框架未解决的问题。批处理方法如数据驱动预测控制需预收集数据集且无非线性动力学稳定性证书；基于信息性的方法离线且非递归地表征数据充分性；两者均未利用网络系统已知图拓扑作为结构先验。本文解决这两个局限。首先，开发流收缩证书beta_cert(t)=beta_hat(t)-rho(t)，其中beta_hat(t)通过对部分输入输出观测的滑动窗口进行积分回归递归估计，rho(t)是将数据相关不确定性半径映射估计误差到真实闭环收缩率保守界的映射。当beta_cert(t)越过并维持在零以上时，证书发出可证明安全的部署信号。其次，引入拓扑感知估计器，将雅可比矩阵上已知图邻接作为精确零约束，将每行有效参数计数从O(N)降至O(d_max)，其中d_max为最大节点度。在具有两个观测节点的重尾拉普拉斯干扰下的五节点非线性基准测试中，流证书从130个样本在t* = 2.6s实现认证部署，比离线批处理基线早17秒，在未受保护窗口期间累积误差低16倍。拓扑感知估计器将认证时间缩短59%（1.62s对3.98s），累积干扰成本降低58%，优势在所有小于40个样本的窗口大小中持续存在。该框架与领域无关，适用于流数据和部分观测下的任何大规模非线性网络系统。
英文摘要
Certifying the safety of a control action in real time, from streaming partial observations of a nonlinear, interconnected system under non-stationary disturbances, is a problem no existing data-driven framework solves. Batch methods such as data-enabled predictive control require a pre-collected dataset and offer no stability certificate for nonlinear dynamics; informativity-based approaches characterize data sufficiency offline and non-recursively; neither exploits the known graph topology of networked systems as a structural prior. This paper addresses both limitations. First, we develop a streaming contraction certificate beta_cert(t) = beta_hat(t) - rho(t), where beta_hat(t) is estimated recursively via integral regression on a sliding window of partial input-output observations, and rho(t) is a data-dependent uncertainty radius mapping estimation error to a conservative bound on the true closed-loop contraction rate. The certificate issues a provably safe deployment signal the moment beta_cert(t) crosses and sustains above zero. Second, we introduce a topology-aware estimator enforcing known graph adjacency as exact zero constraints on the Jacobian, reducing the effective parameter count per row from O(N) to O(d_max) for maximum node degree d_max. On a five-node nonlinear benchmark under heavy-tailed Laplace disturbances with two observed nodes, the streaming certificate achieves certified deployment at t*=2.6s from 130 samples, 17 seconds earlier than an offline batch baseline, with 16x lower accumulated error during the unprotected window. The topology-aware estimator cuts certification time by 59% (1.62s vs 3.98s) and accumulated disturbance cost by 58%, with the advantage persisting across all window sizes below 40 samples. The framework is domain-agnostic and applies to any large-scale nonlinear networked system under streaming data and partial observations.
