{"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/forward-backward-extended-dmd-with-an","title":"Forward-Backward Extended DMD with an Asymptotic Stability Constraint","arxiv_id":"2403.10623","date":"2024-03-15","proceeding":null,"authors":["Louis Lortie","Steven Dahdah","James Richard Forbes"],"abstract":"This paper presents a data-driven method to identify an asymptotically stable Koopman system from noisy data. In particular, the proposed approach combines approximations of the system's forward- and backward-in-time dynamics to reduce bias caused by noisy data while enforcing asymptotic stability. A Koopman model of an inherently asymptotically stable system can be unstable due to noisy data and a poor choice of lifting functions. To prevent identifying an unstable model, the proposed approach imposes an asymptotic stability constraint on the Koopman model. The proposed method is formulated as a semidefinite program and its performance is compared to state-of-the-art methods with a simulated Duffing oscillator dataset and experimental soft robot dataset.","url_abs":"https://arxiv.org/abs/2403.10623v1","url_pdf":"https://arxiv.org/pdf/2403.10623v1.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":"forward-backward-extended-dmd-with-an","repo_url":"https://github.com/decargroup/forward_backward_koopman","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}