0566289 20240402213540.120230104235959.9 10.21136/panm.2022.15 10 s. P cav_un_epca*0566288978-80-85823-73-8163-172PrahaInstitute of Mathematics CAS Prague2023KůsP.PapežJ.RozložníkM.SegethK.ŠístekJ. Dynamical system Singular perturbation Averaging Parameter estimation Slow-fast decomposition Damped oscillations cav_un_auth*0404313 Papáček Štěpán UTIA-B Teorie řízení Department of Control Theory TŘ TR CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0100790 Matonoha Ctirad UIVT-O Oddělení výpočetní matematiky Department of Computational Mathematics Department of Computational Mathematics Ústav informatiky AV ČR, v. v. i. konferenční příspěvek http://library.utia.cas.cz/separaty/2023/TR/papacek-0566289.pdf 295,11 kB GA21-03689S GA ČR CZ cav_un_auth*0410139 Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes. cav_un_auth*0442350 Programs and Algorithms of Numerical Mathematics 21, PANM 21 /2022/ 20220619 20220624 Jablonec nad Nisou CZ BC 10000 10100 10102 2024 2 UIVT-O 10000 10100 10101 PR RVO:67985556 RVO:67985807 https://hdl.handle.net/11104/0337768 S 2023 SCOPUS PUBMED WOS konferenční příspěvek 295,11 kB cav_un_epca*0566288 Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar 978-80-85823-73-8 163 172 Praha Institute of Mathematics CAS Prague 2023 Chleboun J. 340 Kůs P. 340 Papež J. 340 Rozložník M. 340 Segeth K. 340 Šístek J. 340