Continuous-Time Nonlinear System Identification and Model Reduction via Linearization Around a Varying Operating Point

Continuous-Time Nonlinear System Identification and Model Reduction via Linearization Around a Varying Operating Point | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 13 May 2025 V1 Latest version Share on Continuous-Time Nonlinear System Identification and Model Reduction via Linearization Around a Varying Operating Point Authors : Sadegh Ebrahimkhani [email protected] and John Lataire Authors Info & Affiliations https://doi.org/10.22541/au.174713047.76694065/v1 1467 views 165 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper addresses the identification and model reduction of a class of continuous-time Nonlinear (NL) systems through a linearization approach. Although the NL system is considered unknown, we demonstrate that its response to perturbations around a varying operating point can be approximated by a Linear Time-Varying (LTV) system model. We show that this LTV model is the linearization of the NL system around the system trajectory. Then, we demonstrate that the vector of LTV coefficients is the gradient of the NL system, evaluated at the system trajectory. This vector field represents the sensitivity of the NL function (describing the system dynamics) with respect to the input space. By estimating this vector field, we identify a low-dimensional subspace within the input space where the NL function exhibits the most variability. This is achieved by employing the Active Subspace (AS) method, which transforms the high-dimensional input space of the NL system into a lower-dimensional space using the estimated LTV coefficients (gradient vector). Subsequently, the LTV/LPV (Linear Parameter-Varying) approximation of the unknown reduced NL model in the new low-dimensional space is recovered. A new parametrization for the LPV coefficients is introduced to ensure that the LPV model remains the linearized version of an unknown NL system. This LTV/LPV model is then utilized to reconstruct the closed form of the NL system in the new (reduced) coordinates. Finally, the performance of the proposed method is illustrated through numerical examples. Supplementary Material File (wileynjdv5_ama_as.pdf) Download 2.99 MB Information & Authors Information Version history V1 Version 1 13 May 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords active subspace method continuous-time system dimension reduction linearization nonlinear system identification Authors Affiliations Sadegh Ebrahimkhani [email protected] Vrije Universiteit Brussel View all articles by this author John Lataire Vrije Universiteit Brussel View all articles by this author Metrics & Citations Metrics Article Usage 1467 views 165 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Sadegh Ebrahimkhani, John Lataire. Continuous-Time Nonlinear System Identification and Model Reduction via Linearization Around a Varying Operating Point. Authorea . 13 May 2025. DOI: https://doi.org/10.22541/au.174713047.76694065/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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