Streaming Contraction Certificates for Nonlinear Networks: Topology-Aware Data Sufficiency with Partial Observation

Abstract

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.