{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/recurrent-equilibrium-networks-unconstrained","title":"Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness","arxiv_id":"2104.05942","date":"2021-04-13","proceeding":null,"authors":["Max Revay","Ruigang Wang","Ian R. Manchester"],"abstract":"This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees of stability and robustness. All models in the proposed class are contracting -- a strong form of nonlinear stability -- and models can satisfy prescribed incremental integral quadratic constraints (IQC), including Lipschitz bounds and incremental passivity. RENs are otherwise very flexible: they can represent all stable linear systems, all previously-known sets of contracting recurrent neural networks and echo state networks, all deep feedforward neural networks, and all stable Wiener/Hammerstein models, and can approximate all fading-memory and contracting nonlinear systems. RENs are parameterized directly by a vector in R^N, i.e. stability and robustness are ensured without parameter constraints, which simplifies learning since \\HL{generic methods for unconstrained optimization such as stochastic gradient descent and its variants can be used}. The performance and robustness of the new model set is evaluated on benchmark nonlinear system identification problems, and the paper also presents applications in data-driven nonlinear observer design and control with stability guarantees.","url_abs":"https://arxiv.org/abs/2104.05942v3","url_pdf":"https://arxiv.org/pdf/2104.05942v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"recurrent-equilibrium-networks-unconstrained","repo_url":"https://github.com/acfr/RobustNeuralNetworks.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"all","task_name":"All"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2104.05942","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}