Energy shaping of distributed port-Hamiltonian systems based on finite volume approximation

Energy shaping of distributed port-Hamiltonian systems based on finite volume approximation | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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. 10 July 2025 V1 Latest version Share on Energy shaping of distributed port-Hamiltonian systems based on finite volume approximation Authors : Fu Zheng 0000-0001-6129-9251 [email protected] , Ziwei Zhang , and Sizhe Wang Authors Info & Affiliations https://doi.org/10.22541/au.175217762.28401616/v1 278 views 183 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper, we introduce a semi-discrete scheme utilizing a finite volume approximation for a generalized infinite dimensional port-Hamiltonian system (PHS), incorporating boundary control and observation mechanisms through energy shaping and Casimir functions. This approximation yields a family of finite-dimensional input-output systems, whose characteristics vary with the step-size. Notably, these semi-discrete systems retain their PHS properties and Dirac structures in the open-loop configuration. Consequently, these lumped-parameter physical systems can be viewed as approximations of the original infinite-dimensional system. The control of energy shaping is achieved by designing a controller, typically modeled as a finite dimensional PHS interconnected with the port in a power-preserving manner. We also provide a necessary and sufficient condition for the discrete Casimir function. To demonstrate the general methodologies presented in this paper, an example involving the Timoshenko beam is presented. Remarkably, the Casimir function for the continuous beam is successfully reconstructed from its discrete counterparts. Supplementary Material File (energy shaping of distributed port-hamiltonian systems based on finite volume approximation.pdf) Download 758.08 KB Information & Authors Information Version history V1 Version 1 10 July 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords boundary control dirac structure energy shaping infinite dimensional port-hamiltonian system semi-discretization Authors Affiliations Fu Zheng 0000-0001-6129-9251 [email protected] Hainan University View all articles by this author Ziwei Zhang Hainan University View all articles by this author Sizhe Wang Tianjin University View all articles by this author Metrics & Citations Metrics Article Usage 278 views 183 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Fu Zheng, Ziwei Zhang, Sizhe Wang. Energy shaping of distributed port-Hamiltonian systems based on finite volume approximation. Authorea . 10 July 2025. DOI: https://doi.org/10.22541/au.175217762.28401616/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. 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