{"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/uncertainty-modelling-and-robust-observer","title":"Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator","arxiv_id":"2410.01057","date":"2024-10-01","proceeding":null,"authors":["Steven Dahdah","James Richard Forbes"],"abstract":"This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A finite-dimensional approximation of the Koopman operator can be identified directly from data, yielding an approximately linear model of a nonlinear system. The proposed observer synthesis method is made possible by this linearity that in turn allows uncertainty within a population of Koopman models to be quantified in the frequency domain. Using this uncertainty model, linear robust control techniques are used to synthesize robust nonlinear Koopman observers. A population of several dozen motor drives is used to experimentally demonstrate the proposed method. Manufacturing variation is characterized in the frequency domain, and a robust Koopman observer is synthesized using mixed $\\mathcal{H}_2$-$\\mathcal{H}_\\infty$ optimal control.","url_abs":"https://arxiv.org/abs/2410.01057v1","url_pdf":"https://arxiv.org/pdf/2410.01057v1.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":"uncertainty-modelling-and-robust-observer","repo_url":"https://github.com/decargroup/robust_observer_koopman","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"uncertainty-modelling-and-robust-observer","repo_url":"https://github.com/decargroup/pykoop","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}