{"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/identification-of-analytic-nonlinear","title":"Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees","arxiv_id":"2411.00656","date":"2024-11-01","proceeding":null,"authors":["Negin Musavi","Ziyao Guo","Geir Dullerud","YingYing Li"],"abstract":"This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system identification methods: least-squares estimation (LSE), which is a point estimation method; and set-membership estimation (SME), which estimates an uncertainty set that contains the true parameters. We provide non-asymptotic convergence rates for LSE and SME under i.i.d. control inputs and control policies with i.i.d. random perturbations, both of which are considered as non-active-exploration inputs. Compared with the counter-example based on piecewise-affine systems in the literature, the success of non-active exploration in our setting relies on a key assumption on the system dynamics: we require the system functions to be real-analytic. Our results, together with the piecewise-affine counter-example, reveal the importance of differentiability in nonlinear system identification through non-active exploration. Lastly, we numerically compare our theoretical bounds with the empirical performance of LSE and SME on a pendulum example and a quadrotor example.","url_abs":"https://arxiv.org/abs/2411.00656v2","url_pdf":"https://arxiv.org/pdf/2411.00656v2.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":"identification-of-analytic-nonlinear","repo_url":"https://github.com/NeginMusavi/real-analytic-nonlinear-sys-id","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2411.00656","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}