[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86520-en":3,"doc-seo-86520-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86520,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Streaming Contraction Certificates for Nonlinear Networks","Streaming certification of safety for real-time control in nonlinear interconnected systems under non-stationary, heavy-tailed disturbances is addressed for scenarios with only partial input-output observations. Existing data-driven methods rely on pre-collected datasets, lack recursive guarantees, and do not exploit known network topology as a structural prior. A streaming contraction certificate estimates contraction rate recursively via integral regression on a sliding window and issues a provably safe deployment signal when the bound stays above zero. A topology-aware estimator enforces exact Jacobian zero constraints from graph adjacency, reducing parameter count and improving certified deployment speed and robustness.","Streaming Contraction Certificates for Nonlinear Networks: Topology-Aware Data Sufficiency with Partial Observations  \nFaegheh Moazeni 1 ,∗  \narXiv :2607 . 10893v1 [ ee ss . SY] 12 Jul 2026  \nAbstract—Certifying the safety of a control action in realtime, from streaming partial observations of a nonlinear, interconnected system under non-stationary disturbances, is a problem that no existing data-driven framework can solve. Batch methods such as data-enabled predictive control require a pre-collected dataset and provide no stability certificate for nonlinear dynamics; informativity-based approaches characterizedata sufficiency offline and non-recursively; and 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 βcert (t) = ˆβ(t)−ρ(t), where ˆβ(t) is estimated recursively by integral regression on a sliding window of partial input-output observations, and ρ(t) is a datadependent uncertainty radius that maps the estimation error to a conservative bound on the true closed-loop contraction rate. The certificate issues a provably safe deployment signal the moment βcert (t) crosses and sustains above zero. Second, we introduce a topology-aware estimator that enforces known graph adjacency as exact zero constraints on the Jacobian, reducing the effective parameter count per estimation row from O (N) to O (dmax) for maximum node degree dmax. On a five-node nonlinear benchmark under heavy-tailed Laplace disturbances with two observed nodes, the streaming certificate achieves certified deployment at t∗ = 2 .6 s from 130 data samples; 17 seconds earlier than an offline batch baseline and with a lower accumulated error 16 × during the unprotected window. The topology-aware estimator reduces certification time by 59%(1.62 s versus 3.98 s) 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 operating under streaming data and partial observations.  \nI. INTRODUCTION  \nLarge-scale nonlinear networks, e.g., power distribution systems, water distribution networks, urban traffic corridors, and coupled infrastructure systems, generate continuous streams of partial observations through sparse sensor deployments that cover a small fraction of system nodes. Controllers for these systems must be deployed in real time, often under non-stationary and heavy-tailed disturbances, without access to accurate dynamic models. The central challenge is not a shortage of data because modern SCADA systems produce millions of observations per day. The challenge is knowing when the data accumulated so far is sufficient to certify that the next control action will not destabilize the system. That, existing data-driven frameworks cannot answer in real time from partial observations of a nonlinear system.  \nThe author is with the Civil and Environmental Engineering Department at Lehigh University, Bethlehem, PA 18015, USA. Email: [fam321@lehigh.edu](fam321@lehigh.edu)  \n*Corresponding author.  \nContraction theory [1] provides the natural stability language for this problem: a system contracts at rate β > 0 if and only if any two trajectories under the same input converge exponentially, with β computable directly from observed data without requiring an equilibrium or a full system model.  \nRelated Work  \nData informativity and LMI-based synthesis. The data informativity framework of Van Waarde et al. [2] precisely characterizes when a fixed offline dataset is sufficient to certify a control property for linear systems, establishing that stabilization requires strictly less data than identification. De Persis and Tesi [3] showed that data matrices can replace system matrices in linear matrix inequality (LMI)-based controller synthesis, eliminating the identification step entirely. [4] and [5] exten","cbCaia1jG9DBCGZM","https://ap.wps.com/l/cbCaia1jG9DBCGZM","pdf",800897,3,1,6,"English","en",105,"# Abstract\n# Introduction\n## Related Work\n## Data informativity and LMI-based synthesis\n## Behavioral and trajectory-based methods\n## Sparse identification and topology-aware control","[{\"question\":\"What problem does the paper address in real-time control of nonlinear networks?\",\"answer\":\"It addresses how to certify that the next control action will not destabilize a nonlinear interconnected system when only streaming partial input-output observations are available under non-stationary disturbances.\"},{\"question\":\"How does the streaming contraction certificate decide when deployment is safe?\",\"answer\":\"It computes a conservative bound on the true closed-loop contraction rate recursively, then issues a provably safe deployment signal when the certificate becomes positive and remains above zero.\"},{\"question\":\"What advantage does the topology-aware estimator provide?\",\"answer\":\"It uses known graph adjacency to enforce exact zero constraints on the Jacobian, reducing the effective parameter count per estimation row and improving certification time and accumulated disturbance 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problem does the paper address in real-time control of nonlinear networks?","Question",{"text":75,"@type":76},"It addresses how to certify that the next control action will not destabilize a nonlinear interconnected system when only streaming partial input-output observations are available under non-stationary disturbances.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the streaming contraction certificate decide when deployment is safe?",{"text":80,"@type":76},"It computes a conservative bound on the true closed-loop contraction rate recursively, then issues a provably safe deployment signal when the certificate becomes positive and remains above zero.",{"name":82,"@type":73,"acceptedAnswer":83},"What advantage does the topology-aware estimator provide?",{"text":84,"@type":76},"It uses known graph adjacency to enforce exact zero constraints on the Jacobian, reducing the effective parameter count per estimation row and improving certification time and accumulated 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